Steven Weinberg offers a way to explain inflation

[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.

Right. Did you already cite Bonanno's recent paper? It's a good readable review and it mentions the 2000 result of Bonanno and Reuter to that effect.

http://arxiv.org/abs/0911.2727
Astrophysical implications of the Asymptotic Safety Scenario in Quantum Gravity
Alfio Bonanno
(Submitted on 13 Nov 2009)
"In recent years it has emerged that the high energy behavior of gravity could be governed by an ultraviolet non-Gaussian fixed point of the (dimensionless) Newton's constant, whose behavior at high energy is thus antiscreened. This phenomenon has several astrophysical implications. In particular in this article recent works on renormalization group improved cosmologies based upon a renormalization group trajectory of Quantum Einstein Gravity with realistic parameter values will be reviewed. It will be argued that quantum effects can account for the entire entropy of the present Universe in the massless sector and give rise to a phase of inflationary expansion. Moreover the prediction for the final state of the black hole evaporation is a Planck size remnant which is formed in an infinite time."
Comments: 28 pages, 6 figures. Invited talk at Workshop on Continuum and Lattice Approaches to Quantum Gravity. Sept. 2008, Brighton UK. To appear in the Proceedings

The point you were making is around the top of page 18. If the mass is below critical, no horizon exists.

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]

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.

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]

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.

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]

... It’s troublesome only within a window of energies around the Planck scale." http://www.damtp.cam.ac.uk/user/tong/string/string.pdf
...

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.

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".
...

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]

How exactly, if there is no background metric, does one define the scale?
I suspect this is just a minor problem, I may be the only one puzzled by it.

General covariance is a synonym for diffeomorphism invariance (as other parts of the community call it). Maybe someone can help us understand how the scale Lambda is defined in a diffeo invariant context.

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]

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.

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]

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.

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 that's 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 black holes 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]

Agreement about "on the way" heuristics

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.
...

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

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/planckscale/index-video.php?plik=http://panoramix.ift.uni.wroc.pl/~planckscale/video/Day1/1-3.flv&tytul=1.3%20Nicolai
Here's the index to all the videos from the Planck Scale conference
http://www.ift.uni.wroc.pl/~rdurka/planckscale/index-video.php

 

[Finbar]

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 that's 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 black holes 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.

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]

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

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]

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).

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?

 

[atyy]

http://relativity.livingreviews.org/Articles/lrr-2006-5/
"a canonical formulation is anyhow disfavored by the asymptotic safety scenario"

What!?

 

[Haelfix]

"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). "

AD is a UV property of QUANTUM gravity by definition ... You are summing up ladder diagrams and things like that after all. THe peculiarity here is that it effectively looks semiclassical again. The quantum effects which may have been important at the Planck scale as well as the nonperturbative physics, at transplanckian energies, must drop out.

 

[Finbar]

"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). "

AD is a UV property of QUANTUM gravity by definition ... You are summing up ladder diagrams and things like that after all. THe peculiarity here is that it effectively looks semiclassical again. The quantum effects which may have been important at the Planck scale as well as the nonperturbative physics, at transplanckian energies, must drop out.

Who is summing up ladder diagrams in quantum gravity?! you can't go beyond 2 loops in perturbation theory one has to go to effective field theory and work at energies below the Planck scale.

What your saying here is not the case and I assure you you have been mislead.

Please can you cite a paper where ladder diagrams in QG are being computed and the result is that gravity becomes semi-classical again?

 

[Haelfix]

"you can't go beyond 2 loops in perturbation theory one has to go to effective field theory and work at energies below the Planck scale. "

You can sum up however many orders of perturbation theory that you want in gravity, the thing is you may or may not get an underspecified answer (for instance, depending on constants arising from the counterterms of the next order) or alternatively a divergent answer (for E --> infinity). But for E finite, you will get some number. Incidentally that's what AS presuposes. Namely that as you sum up the perturbation theory, there are cancellations that take place within the divergence structure of the theory (so bad '2' loop terms like GS and the Rs coupling will presumably cancel out)

But anyway, here we are talking about a theory of 2 body scattering. The approximation under consideration is where you take the first exchange term with a graviton, and then 'exponentiate' it by summing up all the associated ladder diagrams. For large impact parameters, this approximation is valid and exact (this is the Eikonal regime).

 

[Finbar]

"you can't go beyond 2 loops in perturbation theory one has to go to effective field theory and work at energies below the Planck scale. "

You can sum up however many orders of perturbation theory that you want in gravity, the thing is you may or may not get an underspecified answer (for instance, depending on constants arising from the counterterms of the next order) or alternatively a divergent answer (for E --> infinity). But for E finite, you will get some number. Incidentally that's what AS presuposes. Namely that as you sum up the perturbation theory, there are cancellations that take place within the divergence structure of the theory (so bad '2' loop terms like GS and the Rs coupling will presumably cancel out)

But anyway, here we are talking about a theory of 2 body scattering. The approximation under consideration is where you take the first exchange term with a graviton, and then 'exponentiate' it by summing up all the associated ladder diagrams. For large impact parameters, this approximation is valid and exact (this is the Eikonal regime).

Papers?

I'm not sure that AS presupposes anything. AS is a possible scenario in which taking the cutoff to infinity will give you a finite theory.

I still insist that whatever approximation you are on about is certainly not valid at the UV fixed point of gravity. For sure it neglects non-perturbative effects if your just exponentiating the tree level graviton exchange.

My point has always been that all these arguments based on perturbation theory and the Einstein Hilbert action have nothing to say about AS. The Eikonal regime is sub-plackian
GE<lpl. It says nothing about graviton loops.

Look at fig 1. in http://arxiv.org/pdf/0908.0004v1
Its in the semi circle at the bottom that we need to know QG and can make comments on non-perturbative renormalisation. If AS is realized in nature this regime is controlled by a
UV fixed point and we don't expect black holes to be formed. AD is valid in the strong gravity regime where arguments can be made that we must see black holes here but these arguments have no bearing on the physics of a full non-pertubative theory of QG.

 

[Haelfix]

"The Eikonal regime is sub-plackian GE<lpl"

For the 10 th time.. Its transplanckian : E (CM) >>> Mpl! The papers I have already listed explain this in great detail, or see Veneziano's papers in the 80s (which are cited in Srednicki's paper)

Every point in that semicircle in figure 1 are at transplanckian energies!

 

[Finbar]

"The Eikonal regime is sub-plackian GE<lpl"

For the 10 th time.. Its transplanckian : E (CM) >>> Mpl! The papers I have already listed explain this in great detail, or see Veneziano's papers in the 80s (which are cited in Srednicki's paper)

Every point in that semicircle in figure 1 are at transplanckian energies!

I agree E>>Mpl but this means GE>>lpl because GE is a length not a mass. So we're in the IR physics of gravity 1/GE<<Mpl.

Sorry I meant GE>lpl in my last post.

I know its confusing that there's this UV/IR thing with gravity. But you need to think of the physics here. If I collide two tennis balls together then the energy E>>Mpl but I don't need QG to describe the physics. If I further take the mass of the tennis balls and compact them down such that when they collide there within a radius r<2EG then a black hole must form but the curvature at the horizon will be sub-plackian therefore I can still describe the physics without QG I only need semi-classical physics. Its only when I take a small amount of energy E~Mpl and confine it to a very very tiny space r=2GE~lpl that the curvature becomes Plackian and we need QG. In the Fig. 1 in Giddings paper this is the semi circle with the ? at the bottom left were both E and b are small i.e. a small energy confined to a small radius, its here and only here that the curvature is Plackian and we're in the UV.

 

[Haelfix]

Ok good, we are on the same page then. The regimes are paremetrized by the magnitude of the impact parameter relative to the Schwarzschild radius (well technically some sort of radius between two shockwaves, which is order magnitude the same as the schwarschild radius) and only for the case where b << R do you need to worry about strong coupling effects.. No one knows what goes on there exactly (although you can make the point that you need to smoothly match between regimes)

But the point is a generic field theory of gravity at transplanckian center of mass energies must be able to accommodate black hole states in their spectrum. It doesn't matter that those states are formed in regimes that are effectively classical or semiclassical (at large impact parameters). You still require that the entropy scales as the area, and there you run into a problem b/c at those ultra high energy scales the putative, apparently universal field theory under question has to be conformal and at no point can it have any states that satisfy this type of scaling.

If AS was an effective theory, there would be no problem, b/c you could just argue that you picked the wrong epsilon parameter to perturb around and you don't capture the correct physical regimes, but here this is supposedly *the* theory of all quantum gravity valid at all energy scales with arbitrary matter couplings. It has to be able to have a spectrum that contains high energy black hole states, since we know its low energy behavior is normal GR and will thus also have Eikonal and Coulomb regimes in high energy scattering experiments.

 

[Finbar]

Ok good, we are on the same page then. The regimes are paremetrized by the magnitude of the impact parameter relative to the Schwarzschild radius (well technically some sort of radius between two shockwaves, which is order magnitude the same as the schwarschild radius) and only for the case where b << R do you need to worry about strong coupling effects.. No one knows what goes on there exactly (although you can make the point that you need to smoothly match between regimes)

But the point is a generic field theory of gravity at transplanckian center of mass energies must be able to accommodate black hole states in their spectrum. It doesn't matter that those states are formed in regimes that are effectively classical or semiclassical (at large impact parameters). You still require that the entropy scales as the area, and there you run into a problem b/c at those ultra high energy scales the putative, apparently universal field theory under question has to be conformal and at no point can it have any states that satisfy this type of scaling.

If AS was an effective theory, there would be no problem, b/c you could just argue that you picked the wrong epsilon parameter to perturb around and you don't capture the correct physical regimes, but here this is supposedly *the* theory of all quantum gravity valid at all energy scales with arbitrary matter couplings. It has to be able to have a spectrum that contains high energy black hole states, since we know its low energy behavior is normal GR and will thus also have Eikonal and Coulomb regimes in high energy scattering experiments.

Ok I think we agree on the black hole scattering points now. But we still need to address the entropy scaling. What you said wasn't entirely correct.

A generic fundamental QFT has only to be conformal at the UV fixed point; by definition. So its only at this point that scaling arguments apply. So the question is when and where is physics at the UV fixed point. In gravity it is when the curvature becomes Plackian such that classical physics breaks down and we require UV completion. This happens only at very short distances r<lpl where the Weyl curvature C>Mpl^2. This is the case for the singularity of a generic black hole. But we can only say that all the physics of the black hole is at the UV fixed point when the curvature all the way the way up to the horizon is Plackian. This only happens when the radius of the BH is r~lp.

 

[marcus]

Ok I think we agree on the black hole scattering points now...

Then maybe you would explain something. Can you describe a scattering experiment which, if it were performed and came out as you imagine, would invalidate the AS approach?

 

[Finbar]

Then maybe you would explain something. Can you describe a scattering experiment which, if it were performed and came out as you imagine, would invalidate the AS approach?

There are researchers currently looking into this and I would expect papers to be published sometime in the near future.

This paper may be of some interest http://arxiv.org/pdf/0707.3983

 

[atyy]

Look at fig 1. in http://arxiv.org/pdf/0908.0004v1

A generic fundamental QFT has only to be conformal at the UV fixed point; by definition. So its only at this point that scaling arguments apply. So the question is when and where is physics at the UV fixed point. In gravity it is when the curvature becomes Plackian such that classical physics breaks down and we require UV completion. This happens only at very short distances r<lpl where the Weyl curvature C>Mpl^2. This is the case for the singularity of a generic black hole. But we can only say that all the physics of the black hole is at the UV fixed point when the curvature all the way the way up to the horizon is Plackian. This only happens when the radius of the BH is r~lp.

In fig 1 if I fix impact parameter and move to higher and higher energies, I'll move into the the strong gravity or classical black hole region. Won't I need the UV completion at this point - the classical theory won't work because we expect Hawking radiation from thermodynamics, and semi-classical theory won't work because of information loss?

 

[atyy]

I've asked this before, but still don't understand the answer, so here it is again. The UV fixed point should be scale invariant - under what assumptions is that equivalent to conformal invariance?

 

[Finbar]

In fig 1 if I fix impact parameter and move to higher and higher energies, I'll move into the the strong gravity or classical black hole region. Won't I need the UV completion at this point - the classical theory won't work because we expect Hawking radiation from thermodynamics, and semi-classical theory won't work because of information loss?

Ok so if we're in the semi-classical regime the black hole is radiating so the horizon shrinks. But as it shrinks and the horizon approaches the Planck length and the temperature approaches the Planck mass we then need a UV completion.

So far AS "solves" the information paradox by saying that the information is stored in a Planck size remnant. But I don't think this is a satisfactory solution.

 

[atyy]

Ok so if we're in the semi-classical regime the black hole is radiating so the horizon shrinks. But as it shrinks and the horizon approaches the Planck length and the temperature approaches the Planck mass we then need a UV completion.

So far AS "solves" the information paradox by saying that the information is stored in a Planck size remnant. But I don't think this is a satisfactory solution.

Hmmm, let me think about that. I was hoping that AS would prevent high energy scattering experiments by allowing only asymptotically dS spaces by enforcing a positive cosmological constant through the renormalization flow. (No, I don't really know what I'm talking about.)

What's wrong with the remnant solution?

 

[Finbar]

I've asked this before, but still don't understand the answer, so here it is again. The UV fixed point should be scale invariant - under what assumptions is that equivalent to conformal invariance?

I think that scale invariance is a sub group of conformal in variance. But I'm not sure. So if a theory is conformal in the UV it has to be scale invariant and hence at a fixed point.

 

[atyy]

I think that scale invariance is a sub group of conformal in variance. But I'm not sure. So if a theory is conformal in the UV it has to be scale invariant and hence at a fixed point.

Yes, I think that's true. What I don't understand is why the UV fixed point must be conformal, though I understand it has to be scale invariant. I think that under some additional assumptions like unitarity, Poincare invariance or something, then scale invariant theories are conformal - but I don't know what the exact conditions are.

Eg. http://arxiv.org/abs/hep-th/0504197 or footnote 3 of http://arxiv.org/abs/0909.0518

 

[Finbar]

Hmmm, let me think about that. I was hoping that AS would prevent high energy scattering experiments by allowing only asymptotically dS spaces by enforcing a positive cosmological constant through the renormalization flow. (No, I don't really know what I'm talking about.)

What's wrong with the remnant solution?

http://arxiv.org/pdf/hep-th/9508151

The Black Hole Information Paradox
Steven B. Giddings†
Department of Physics University of California Santa Barbara, CA 93106-9530
Abstract
A concise survey of the black hole information paradox and its current status is given. A summary is also given of recent arguments against remnants. The assumptions underly- ing remnants, namely unitarity and causality, would imply that Reissner Nordstrom black holes have infinite internal states. These can be argued to lead to an unacceptable infinite production rate of such black holes in background fields.
(To appear in the proceedings of the PASCOS symposium/Johns Hopkins Workshop, Baltimore, MD, March 22-25, 1995).


Theres also a another paper by Giddings but I can't find it right now

 

[marcus]

The paper by Weinberg which is our topic is
http://arxiv.org/abs/0911.3165
Asymptotically Safe Inflation
Steven Weinberg
13 pages
(Submitted on 16 Nov 2009)
"Inflation is studied in the context of asymptotically safe theories of gravitation. It is found to be possible under several circumstances to have a long period of nearly exponential expansion that eventually comes to an end."
================

The basic idea is to explain a self-terminating inflation episode, without making up some exotic "inflaton" matter field, as a natural consequence of the running of couplings such as Newton's G. The couplings can be assumed to be at or near their UV limit at the start of expansion. And this by itself, Weinberg shows, is sufficient to cause exponential expansion.

We can think of the scale as related to density. As the universe expands, the density falls off, and the couplings depart from their values at the UV-limit. After some 60 e-foldings of expansion the density is low enough that inflation ends.

Some readers may wish to question this statement of Weinberg:

"We will work with a completely general generally covariant theory of gravitation. (For simplicity matter will be ignored here, but its inclusion would make no important difference.)"

More about matter in the context of Asymptotic Safety is here:
https://www.physicsforums.com/showthread.php?t=349513
in the "Grav. + GUT" thread.

 

[uniquo87]

I would like to know the derivation of the field equations of quantum electrodynamics.

 

[marcus]

We should try to get this thread back on track as per the original Weinberg paper.

There is no physical reason to assume black holes are especially relevant or significant in this context, and the Weinberg paper is not about black holes. It is about inflation. Asymsafe QG provides a neat and economical way to explain inflation.

Since I started the thread a great paper by Shaposhnikov and Wetterich has come out. http://arxiv.org/abs/0912.0208 I'll quote some excerpts. Here's from page 2.

From the studies of the functional renormalization group for Γ_k one infers a characteristic scale dependence of the gravitational constant or Planck mass,

M_P² (k) = M_P² + 2ξ₀k²​

where M_P = (8πG_N )^−1/2 = 2.4 × 10¹⁸ GeV is the low energy Planck mass, and ξ₀ is a pure number, the exact value of which is not essential for our considerations.

From investigations of simple truncations of pure gravity one finds ξ₀ ≈ 0.024 from a numerical solution of FRGE [5, 11, 12]. For scattering with large momentum transfer q the effective infrared cutoff k² is replaced by q² . Thus for q² ≫ M_P² the effective gravitational constant G_N(q² ) scales as 1/(16πξ₀q²) , ensuring the regular behavior of high energy scattering amplitudes.