Steven Weinberg offers a way to explain inflation

[atyy]

Atyy gave a concise account. In much of field theory you keep the same formula, you just gradually change the parameters you plug into it.

The "form of the Lagrangian" remains the same, but its coupling constants "run" as the relevant energy ramps up, or as you zoom the microscope in.

A reference that I've found very useful is Kardar's statistical mechanics notes. In his exposition, we start with all possible terms having the symmetries we know of experimentally (http://ocw.mit.edu/NR/rdonlyres/Physics/8-334Spring-2008/7507574B-4ADC-4611-8058-5985074514A8/0/lec7.pdf ) - because "We also discovered that even if some of these terms are left out of the original Hamiltonian,they are generated under coarse graining (http://ocw.mit.edu/NR/rdonlyres/Physics/8-334Spring-2008/109D498F-09AA-4503-ACFB-C9657CF2B157/0/lec12.pdf )." - in other words, the calculations show that the coupling constants run as you zoom the microscope out.

Although this is statistical mechanics, not quantum field theory, Weinberg's Asymptotic Safety proposal resulted from him trying to learn statistical field theory. http://ccdb4fs.kek.jp/cgi-bin/img/allpdf?197610218

 

[Finbar]

It troubles me slightly that people still seem unsure as to whether couplings run or whether the renormalisation group is physical. These are well tested facts and Kenneth Wilson was awarded the Noble prize for his work on the renormalisation group.

I would go as far as saying that if you don't understand the renormalisation group you don't understand QFT. Sure you can mindlessly compute scattering amplitudes computing Feynman diagrams but this only tells you stuff about scattering phenomena in some man made experiment. Real physics like the confinement of quarks needs a full non-perturbabtive understanding of QFT which we still lack. Our best tools to approach these problems come from the lattice and renormalisation group techniques.

 

[friend]

The "form of the Lagrangian" remains the same, but its coupling constants "run" as the relevant energy ramps up, or as you zoom the microscope in.

Aren't mass and charge also compling constants. Do you mean that these can change with scale? I don't know any reason why they shouldn't change.

If the "constants" change, then does this just make them another kind of field in QFT? Or are the parameters that change the "constants" not the same as the spacetime coordinates of QFT? You did mention scale which depends on spacetime coordinates.

 

[atyy]

Aren't mass and charge also compling constants. Do you mean that these can change with scale? I don't know any reason why they shouldn't change.

If the "constants" change, then does this just make them another kind of field in QFT? Or are the parameters that change the "constants" not the same as the spacetime coordinates of QFT? You did mention scale which depends on spacetime coordinates.

Let's say you have a theory in which fundamentally everything is a bunch of classical point masses connected by classical springs with spring constant k. But if you cannot experimentally manipulate neighbouring points (high energy or small scale), and can only manipulate far away points (low energy or large scale), then you will get some effective spring constant spring constant k' when you treat the multiple in between springs as one spring, so the coupling constant will run with energy or scale.

http://en.wikipedia.org/wiki/Hooke's_law

 

[marcus]

Aren't mass and charge also compling constants. Do you mean that these can change with scale? I don't know any reason why they shouldn't change.

If the "constants" change, then does this just make them another kind of field in QFT? Or are the parameters that change the "constants" not the same as the spacetime coordinates of QFT? You did mention scale which depends on spacetime coordinates.

The constant (say a mass) is constant through-out space and time. It does not depend on the coordinates. It only depends on the scale---which can be an energy or scale of spatial resolution.

Imagine looking at the whole process at one scale, and then look again at a closer scale, as with a zoom microscope. Or photographing a motion picture with finer and finer pixels.

You have probably heard of the "bare" mass of a particle as contrasted to the mass measured at low energy and macroscopic distance.

You probably know that in QED (quantum electrodynamics) there is this important number which is NOT always 1/137. That is only the macroscopic low energy value, for when the two electrons never get very close to each other. If you increase the energy of the collision, or decrease the distance scale of the encounter, then the correct number gets larger, like 1/135, or 1/133.

None of this variation depends on spacetime coordinates, it does not vary with position. It varies only with the degree of coarseness or refinement with which one is viewing the process. Alternatively, the characteristic energy of an interaction. Because if you fire two things at each other with more energy, they get closer. Energy and length are in an inverse relation.

 

[friend]

None of this variation depends on spacetime coordinates, it does not vary with position. It varies only with the degree of coarseness or refinement with which one is viewing the process.

The only way I can (presently) imagine this is if, say, the interval of integration in the path integral changes from minus to plus infinity to something smaller. Then I can understand how the coupling constants would change. Is this what's going on?

 

[marcus]

The only way I can (presently) imagine this is if, say, the interval of integration in the path integral changes from minus to plus infinity to something smaller. Then I can understand how the coupling constants would change. Is this what's going on?

You can ask Finbar or Atyy to explain it more rigorously. To me this "scale" is an embryonic idea which is growing in the mind of physics and which has already shown enormous practical validity, so that it must correspond to something real---which however is as yet not fully defined. It dates from the seminal work of Ken Wilson in the 1970s (But Atyy traces the idea back further in other kinds of physics, not particle.) And just two weeks ago at the Perimeter conference, Vincent Rivasseau presented a different way to think about scale and a different reasoning about how things run with scale. So I think of it as ongoing work in progress, how we think about this.

Let's see if we can find something about the running of the fine structure constant. I couldn't find anything in Wikipedia the first time I tried but I found a study that said that the value could get as high as 1/128.96.
So roughly the fine structure constant at very high energies is around 1/129, instead of 1/137. Maybe somebody else has a good source for this.

 

[atyy]

The only way I can (presently) imagine this is if, say, the interval of integration in the path integral changes from minus to plus infinity to something smaller. Then I can understand how the coupling constants would change. Is this what's going on?

Yes. Take a look at Eq (A.1) and (A.2) of http://relativity.livingreviews.org/Articles/lrr-2006-5/ . The LHS of (A.1) is taken over everything less than Lambda, while the RHS is taken over everything less than (Lamda-dl), because you coarse grained over dl as defined in (A.2).

You may also find useful Hollowood's notes about how the usual bizarre description of renormalization is related to Wilsonian common sense. http://arxiv.org/abs/0909.0859

 

[friend]

Yes. Take a look at Eq (A.1) and (A.2) of http://relativity.livingreviews.org/Articles/lrr-2006-5/ . The LHS of (A.1) is taken over everything less than Lambda, while the RHS is taken over everything less than (Lamda-dl), because you coarse grained over dl as defined in (A.2).

So you're saying the constants change because of coarse graining the integration variables? Or is there more to it than that? Thanks.

 

[atyy]

So you're saying the constants change because of coarse graining the integration variable? Or is there more to it than that? Thanks.

That's all. Very simple conceptually, but very demanding technically.

 

[marcus]

That sounds a deal more sensible, and satisfactory to friend, than what I had to say. I'd erase my posts that struggle with the idea of renormalization group flow, except I still find it mysterious.

 

[friend]

That's all. Very simple conceptually, but very demanding technically.

And a coarser grain means you're looking at a smaller scale?

Is this more demanding because they're trying to solve this coarse graining analytically instead of numerically on a computer?

 

[atyy]

And a coarser grain means you're looking at a smaller scale?

Larger scale. The renormalization flow is by convention taken over coarser and coarser grain, less and less resolution. So generally you lose information, and you cannot get back to the high energy theory. But if we're lucky, as Asymptotic Safety postulates, we can run the renormalization flow backwards to finer and finer scales, and we can figure out the theory at arbitrarily high energies.

Is this more demanding because they're trying to solve this coarse graining analytically instead of numerically on a computer?

I just meant more demanding because the devil is in the details. I was thinking analytically, not numerically, and I don't know if numerics would necessarily be less gruesome. But numerics can help - eg. in Xiao-Gang Wen's approach, the analytical approach he uses that indicates he may have gravitons emerging from spins on a lattice is unreliable, and he indicates on his last slide that he therefore needs numerics to see if his analytics hasn't misled him. http://dao.mit.edu/~wen/talks/09UBC-long.pdf

 

[Finbar]

The only way I can (presently) imagine this is if, say, the interval of integration in the path integral changes from minus to plus infinity to something smaller. Then I can understand how the coupling constants would change. Is this what's going on?

Yeah that's pretty much how it works. You put in a cutoff at some energy scale and then integrate only up to the cutoff. Then you can find that your coupling constants depend on the value of the cutoff. Look in Peskin and Schroeder(or another book) its explained quite nicely in there. If you understand the path integral formalism of QFT then it should be pretty easy to follow. I think once you see a few examples using the path integral it makes sense and then you really understand what renormalisation is in physical terms. Before Wilson people thought renormalisation was just some trick but really its a very physical thing. In terms of QFT its really a generalisation of the uncertainty principle.

If you think of QED the closer you look at a group of electrons then the higher the uncertainty in the energy of the field and hence the number of electrons. The beauty of the renormalisation group is that you can essentially encode this uncertainty into the running of the electric charge.

 

[atyy]

That sounds a deal more sensible, and satisfactory to friend, than what I had to say. I'd erase my posts that struggle with the idea of renormalization group flow, except I still find it mysterious.

Well, if you listen to Zinn-Justin's talk at the AS conference, there is still something mysterious. In condensed matter to get to the fixed point, you have to tune one (or a few parameters) such as the temperature - and of course, in condensed matter it's no mystery who tunes it - the experimenter! So he goes on and on about fine tuning at the end of his lecture. But I don't really understand this issue, just reporting here.

 

[Haelfix]

"The paper does't say anywhere that the action in the UV will be Einstein-Hilbert."

Umm, from the abstract
"The argument is based on black-hole domination of the high energy spectrum of gravity "

Later

"However, our experience with gravity has shown that once enough energy is concentrated
in a given region a black hole will form. As far as our understanding goes, the high energy spectrum of GR is dominated by black holes. More technically, it is expected that in theories of gravity, black holes will provide the dominant contribution to the large energy
asymptotics of the density of states as a function of the energy. "

And they go on to write down a classical Schwarzschild solution for their high energy scaling behaviour. Thats EH gravity...

Anyway, trivially all of this was known long before this paper reviewed it. Asymptotic darkness has a tension with universal field theories (whether free or safe). Something has to give. The AD scenario is pretty airtight from an SMatrix and thermodynamic point of view (even string theorists concede that it replaces their theory at transplanckian energies), the question is how do you smoothly interpolate between the regimes. Losing a dimension of space is a highly destructive operation to have take place. All the degrees of freedom of the extra dimension must conspire to cancel somehow (nonlocally), and so forth.

 

[Bob_for_short]

Personally I like running constants a lot.

And I don't. I call them "ran constants" because they feel so. They want to be just constants but many theorists make them run to make ends meet. Although it is a crying rubbish, some theorists show themselves off as cool.

 

[MTd2]

Losing a dimension of space is a highly destructive operation to have take place. All the degrees of freedom of the extra dimension must conspire to cancel somehow (nonlocally), and so forth.

A magical cancellation of the infinite degrees of freedom is really what happens. But I don`t this is how you should visualize the transition from 4 to a lower dimension. One should visualize that as one magnifies a microscope, one would see and increasingly intense bubbling, in a high pressure pan.

Imagine that the Planck scale is a microscopic zoom into what happens in the critical point, approaching from the liquid phase state domain. You`d see a liquid drop, the so called 2 dimensions. Do not count the inside the liquid, because one cannot get smaller than that scale.

If you get a little farther, that is, you simultaneously demagnify and get away from the critical point, you`d see more regions merged, and more merged liquid drop, and bit more freedom to navigate inside them, since they are not of the smallest size. There are many kinds of merged drops, including single drops. Than you average that out, and statistically find a fractal dimension. As you approach normal pressure and ambient temperature, you pretty much recover 3 dimensions, in the case of water. Or 4, in the case of gravitation.

But I guess that the number of dimensions of an even horizon and the little drop are not coincidences. One is probing a region of space with an energy close to that of a plank scale, then I think you can imagine the liquid drop as little white hole. The black hole would be the remaining gas regions.

 

[MTd2]

I am sorry, I meant critical point, not triple point.

 

[Finbar]

"The paper does't say anywhere that the action in the UV will be Einstein-Hilbert."

Umm, from the abstract
"The argument is based on black-hole domination of the high energy spectrum of gravity "

Later

"However, our experience with gravity has shown that once enough energy is concentrated
in a given region a black hole will form. As far as our understanding goes, the high energy spectrum of GR is dominated by black holes. More technically, it is expected that in theories of gravity, black holes will provide the dominant contribution to the large energy
asymptotics of the density of states as a function of the energy. "

And they go on to write down a classical Schwarzschild solution for their high energy scaling behaviour. Thats EH gravity...

Anyway, trivially all of this was known long before this paper reviewed it. Asymptotic darkness has a tension with universal field theories (whether free or safe). Something has to give. The AD scenario is pretty airtight from an SMatrix and thermodynamic point of view (even string theorists concede that it replaces their theory at transplanckian energies), the question is how do you smoothly interpolate between the regimes. Losing a dimension of space is a highly destructive operation to have take place. All the degrees of freedom of the extra dimension must conspire to cancel somehow (nonlocally), and so forth.

Again they are at no point assuming that at high energies the action will be Einstein Hilbert.
They are assuming, however, that what ever the action is it will still have black hole solutions. No, where do they offer any argument to support this assumption. Reuter and Bonanno have shown that if gravity is Asymptotically safe there is a lower limit of order the black mass for which black holes do not form. Hence we do not expect the entropy to run as the area at the UV fixed point.

The argument against Asymptotic safety, Asymptotic darkness, is based on an assumption and hence the argument is only as strong as this assumption.

 

[Finbar]

And I don't. I call them "ran constants" because they feel so. They want to be just constants but many theorists make them run to make ends meet. Although it is a crying rubbish, some theorists show themselves off as cool.

Its a experimental fact that constants run. Whether you like them or not is neither here nor there; they are fact.

 

[Haelfix]

Again they are at no point assuming that at high energies the action will be Einstein Hilbert.
They are assuming, however, that what ever the action is it will still have black hole solutions.
The argument against Asymptotic safety, Asymptotic darkness, is based on an assumption and hence the argument is only as strong as this assumption.

Who is 'they'?

Anyway, the argument that high energy scattering is dominated by black hole production is robust and the paper doesn't go into detail about it, b/c many hundreds of other papers have been written on the subject. Its a very generic expectation, and is based on thermodynamic and SMatrix arguments and is quite insensitive to the details of which formalism you pick (string vs field vs whatever). The simplest of these is to simply assume whatever black holes are created are analogous to EH black holes, but you can pick another action if you so choose.. For instance the recent 2+1 gravity papers by Witten et al argue that there are extra hidden 'BTZ' black hole states in the spectrum, this despite having no propagating degrees of freedom that are naively apparent.

Regardless, if there are indeed black holes in the spectrum of AS (for the reasons listed in the papers I linked), then its almost guarenteed that they will be morally similar to the usual ones we are familiar with, since the underlying action is EH to begin with. A fixed point changes some of the physics, but not so much that black hole physics radically changes (eg no horizons, or Hawking-Bekenstein area law etc etc).

Anyway the more likely explanation if AS is true, is that somehow you lose a dimension of spacetime so the scaling meshes. This isn't completely unprecedented (we've seen strongly coupled field theories with 'emergent' extra dimensions before, for instance in the AdS/CFT case or in N = 8 Supergravity case) but it definitely is a little at odds with standard renormalization group lore and most of our experience with fixed points.

 

[Finbar]

Who is 'they'?

Anyway, the argument that high energy scattering is dominated by black hole production is robust and the paper doesn't go into detail about it, b/c many hundreds of other papers have been written on the subject.

They is Banks, Shomer etc.
Which papers? Why are they not cited? I put it to you that no such robust argument exists.
Nobody knows the UV completion of gravity so how can you write a paper on it.

Sorry but this is science. You can't make an assumption and then present conclusions, based on your assumption, as if they are fact.

I'll tell you what the honest conclusion of the paper I cited should. If gravity is not asymptotically safe then gravity is most likely not described by a QFT and black holes will dominate high energy scattering. However if gravity is Asymptotically safe and this is realized in nature then high energy scattering will be controlled by a fixed point and will not be dominated by black holes.

 

[Haelfix]

They are cited, I listed some already, and if you Hep search for some related terms (high energy black hole production, transplanckian collisions, super Planckian effects, asymptotic darkness) you will find literally hundreds of papers. I do not know of a review article on the subject, but its well known in the biz and by the gravity specialists. The theory group at my university have given talks about this several times before (in different contexts) that I have attended and its a well known expectation with multiple lines of analysis dating back quite a way. Similar to holography, its just one of those things that has a lot of history to it and where you won't find every single argument concisely laid out.

Fishler and Banks are a few modern popularizers.. Eg scenarios like hep-th/0111142 but it probably goes back to Thorne and Hawking and work on inflation.

Anyway gr-qc/0201034 is a good place to start. Also modern realizations, like the large extra dimensions scenarios where black holes are produced at TeV scales are also quite popular (and caused a lot of headaches for CERN in passing)

 

[atyy]

Reuter and Bonanno have shown that if gravity is Asymptotically safe there is a lower limit of order the black mass for which black holes do not form.

Which paper is this?

 

[marcus]

Here's the initial post of the thread. I want to make an adjustment in the notation.

Mtd2 spotted this paper by Steven Weinberg that just went on arxiv.
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."

It could be an important paper, and in any case it's kind of elegant because the inflation episode occurs naturally, by the running of constants, without having to dream up some exotic matter field.

Reuter and Bonanno already proposed something along these lines. The essential arithmetic is very simple: there is evidence of the existence of a UV fixed point for gravity where the dimensionless forms of G(k) the running Newton and Lambda(k) the running dark energy constant both converge to finite values as the length scale k -> 0

But one can see by simple dimensional reasoning that their dimensionless forms are
G(k)/k² and Lambda(k)k².

So for them to go to finite limits as k->0 we must have G(k) getting very small and Lambda(k) growing enormous.

That's just the thing to cause rapid expansion. The Newton constant is almost nothing, so nothing to hold the geometry together, and the cosmological constant---the dark energy that accelerates expansion---totally huge.

But as inflation proceeds the scale k increases, which increases G and reduces Lambda. So the process eventually (actually quite quickly) shuts itself off.

Let me change the convention and make the scale k a momentum. That will conform with Percacci's FAQ, valuable handy resource that it is.
So then the dimensionless form of Newton constant is G(k)k².
And the dimensionless form of cosmo constant is Λ(k)/k².

It's the obvious change because momentum is the reciprocal of length (we have hbar=c=1).
And now approaching the UV fix point means k goes to infinity, whereas before we had the length scale going to zero.

The main topic here in this thread is what Weinberg has said recently about the asymsafe idea---and his current research on it, applied to cosmology. And the application to explaining inflation in particular.

I wanted to recall the initial post so we don't get too far off and completely forget the topic.

Just now, though, Atyy asked Finbar about the QG black hole mass threshhold. I recall a Bojowald paper with that as tentative result back in 2005 and one could find more recent sources by seeing who has cited the Bojowald 2005 paper. Ben Ward has cited it several times, and he does asymptotic safety-related research. I personally don't know anything conclusive in this department but for what its worth here is a lead.
http://arxiv.org/abs/gr-qc/0503041
A black hole mass threshold from non-singular quantum gravitational collapse
Martin Bojowald, Rituparno Goswami, Roy Maartens, Parampreet Singh
(Submitted on 9 Mar 2005)
"Quantum gravity is expected to remove the classical singularity that arises as the end-state of gravitational collapse. To investigate this, we work with a toy model of a collapsing homogeneous scalar field. We show that non-perturbative semi-classical effects of Loop Quantum Gravity cause a bounce and remove the black hole singularity. Furthermore, we find a critical threshold scale, below which no horizon forms -- quantum gravity may exclude very small astrophysical black holes."

The Bojowald paper has been cited in 42 other papers
http://arxiv.org/cits/gr-qc/0503041
I guess anyone of them could carry this idea of a mass threshold forward. The threshold was around the Planck mass.

Finbar mentioned Bonanno and Reuter. The idea of a black hole mass threshold can have occurred in several different contexts. I'm looking forward to seeing some references from the Reuter direction.
Whoah! Here's a Bonanno Reuter paper about this that goes as far back as 2000!

http://arxiv.org/abs/hep-th/0002196
Renormalization group improved black hole spacetimes
A. Bonanno, M. Reuter
46 pages, 7 figures
(Submitted on 23 Feb 2000)
"We study the quantum gravitational effects in spherically symmetric black hole spacetimes. The effective quantum spacetime felt by a point-like test mass is constructed by 'renormalization group improving'' the Schwarzschild metric. The key ingredient is the running Newton constant which is obtained from the exact evolution equation for the effective average action. The conformal structure of the quantum spacetime depends on its ADM-mass M and it is similar to that of the classical Reissner-Nordstrom black hole. For M larger than, equal to, and smaller than a certain critical mass M_{\rm cr} the spacetime has two, one and no horizon(s), respectively. Its Hawking temperature, specific heat capacity and entropy are computed as a function of M. It is argued that the black hole evaporation stops when M approaches M_{\rm cr} which is of the order of the Planck mass. In this manner a 'cold' soliton-like remnant with the near-horizon geometry of AdS_2\times S^2 is formed. As a consequence of the quantum effects, the classical singularity at r=0 is either removed completely or it is at least much milder than classically; in the first case the quantum spacetime has a smooth de Sitter core which would be in accord with the cosmic censorship hypothesis even if M < M_{\rm cr}."

 

[marcus]

We should explore a bit more what the present thread topic is actually about. And what Weinberg's paper is actually about. It is important to keep in mind that the scale k is not a number. It is a physical quantity.

Let me change the convention and make the scale k a momentum. That will conform with Percacci's FAQ, valuable handy resource that it is.
So then the dimensionless form of Newton constant is G(k)k².
And the dimensionless form of cosmo constant is Λ(k)/k².

It's the obvious change because momentum is the reciprocal of length (we have hbar=c=1).
And now approaching the UV fix point means k goes to infinity, whereas before we had the length scale going to zero.

On the other hand G(k)k² is a number and G(k)k² -> G* as k->infty.

G* is a small positive number, we have estimates for it in various Percacci papers.

Now let's express the momentum k in Planck units. Of course Planck units run since G does.
We can simply set
G(k)k² = G*, the value at the limit, and solve for k in terms of the Planck momentum which is sqrt(1/G(k)).
We find that k ~ sqrt(G*) times the Planck momentum as k goes to infinity

Or, equivalently the length 1/k approaches sqrt(1/G*) times the Planck length, again as k goes to infinity (that is, "in the UV").
================
In this post I am just paraphrasing from Percacci's FAQ. He makes the point that whether you consider something discrete or continuous can sometimes depend on what units you choose. If you choose Planck units, then there may turn out to be a minimal length and things may look and act discrete, even though you set them up as a continuum. Interesting FAQ.

 

[Finbar]

They are cited, I listed some already, and if you Hep search for some related terms (high energy black hole production, transplanckian collisions, super Planckian effects, asymptotic darkness) you will find literally hundreds of papers. I do not know of a review article on the subject, but its well known in the biz and by the gravity specialists. The theory group at my university have given talks about this several times before (in different contexts) that I have attended and its a well known expectation with multiple lines of analysis dating back quite a way. Similar to holography, its just one of those things that has a lot of history to it and where you won't find every single argument concisely laid out.

Fishler and Banks are a few modern popularizers.. Eg scenarios like hep-th/0111142 but it probably goes back to Thorne and Hawking and work on inflation.

Anyway gr-qc/0201034 is a good place to start. Also modern realizations, like the large extra dimensions scenarios where black holes are produced at TeV scales are also quite popular (and caused a lot of headaches for CERN in passing)

I'm not questioning holography or any other semi-classial phenomena. The assumption that I'm questioning is about quantum gravity in the UV where all these notions may well breakdown. The best we can do is take our favourite model of QG and try and see how it behaves at high energies.

 

[Haelfix]

Here is another paper on the SMatrix properties of high energy gravitational scattering:
arXiv:0711.5012.

The assumptions are pretty generic, eg the existence of an SMatrix, analyticity, unitarity of black hole time evolution and Lorentz invariance. They analyze the nature of the ultra high (transPlanckian) energy collisions at different impact parameters (Coulomb, Eikonal and strong regimes), and while they do make an ansatz for the strong regime, you can see that by consistency it can't be too far removed b/c it has to match smoothly with the other 2.

Regardless, the Coulomb and Eikonal regime matches closely with the classical shock wave picture of black hole formation, and those regimes at least have to be present in any theory of quantum gravity (where by that one means that 'it' does not modify general relativity and quantum mechanics significantly).

Thus you will still have significant amounts of black hole production at those very high energies, at least so long as you believe in the semiclassical analysis, and this is quite insensitive to substructure, and details of the theory (for instance string theory have different subregimes)

 

[atyy]

The assumptions are pretty generic, eg the existence of an SMatrix

So if AS really predicts something different from Asymptotic Darkness, would that jive with AS working only in de Sitter space where there is no SMatrix, since AS apparently requires the cosmological constant to have some non-zero value from renormalization, and also if we believe the indications from CDT?

 

[Haelfix]

As far as I know that's correct, asymptotic darkness most likely needs flat or anti desitter space to be made sense off. The presence of a positive cosmological constant kills most of the technical assumptions and arguments that goes into it, at least that I am aware off (I am not a gravity specialist).

But I think that's true for most things in quantum gravity. The fate of holography, unitarity, causality, the arrow of time and generalized thermodynamics, and the like are a complete mystery in ds space.

Hell, a lot of gravity people believe that no quantum theory of DeSitter space even exists (again on general quantum mechanics grounds).. No obvious observables, possibly a finite hilbert space, problems with entropy and black holes, etc etc

 

[marcus]

As far as I know that's correct, asymptotic darkness most likely needs flat or anti desitter space to be made sense off. The presence of a positive cosmological constant kills most of the technical assumptions and arguments that goes into it, at least that I am aware off (I am not a gravity specialist).

But I think that's true for most things in quantum gravity. The fate of holography, unitarity, causality, the arrow of time and generalized thermodynamics, and the like are a complete mystery in ds space.

Hell, a lot of gravity people believe that no quantum theory of DeSitter space even exists (again on general quantum mechanics grounds).. No obvious observables, possibly a finite hilbert space, problems with entropy and black holes, etc etc

The presence of a positive cosmological constant kills, you say, the technical support for asymptotic darkness.

Then you generalize: you think "that's true for most things in quantum gravity." That would mean a positive Lambda kills the technical support for most things which you then mention.

You seem to be saying that the presence of a positive cosmological constant is inimical to unitarity, causality, and the arrow of time. Or that acceptance of the presence of a positive cosmological constant is so disastrous to our understanding that we are virtually compelled to deny it as a possibility.
As it stands, without any further explanation, that seems peculiar.

Also your post seems to equate the universe having a positive cosmological constant with our universe being deSitter space. But deSitter space contains no matter. There is no big bang in deSitter space, at least as we usually think of it. dSitter space is far from being the only solution with a positive cosmological constant---it's an idealized special case.

 

[Finbar]

Here is another paper on the SMatrix properties of high energy gravitational scattering:
arXiv:0711.5012.

The assumptions are pretty generic, eg the existence of an SMatrix, analyticity, unitarity of black hole time evolution and Lorentz invariance. They analyze the nature of the ultra high (transPlanckian) energy collisions at different impact parameters (Coulomb, Eikonal and strong regimes), and while they do make an ansatz for the strong regime, you can see that by consistency it can't be too far removed b/c it has to match smoothly with the other 2.

Regardless, the Coulomb and Eikonal regime matches closely with the classical shock wave picture of black hole formation, and those regimes at least have to be present in any theory of quantum gravity (where by that one means that 'it' does not modify general relativity and quantum mechanics significantly).

Thus you will still have significant amounts of black hole production at those very high energies, at least so long as you believe in the semiclassical analysis, and this is quite insensitive to substructure, and details of the theory (for instance string theory have different subregimes)

Yes I like this paper. Thanks for bringing it to my attention.

So here's the thing, you will enter this strong gravity regime where black holes inevitably form. But what is important is not the formation of the black hole, since black holes form classically anyway, what matters, in terms of the scaling of the entropy, is the curvature at the horizon. Its only when the curvature at the horizon is Planckian that the semi-classical thermodynamics breaks down. The larger the energy of the black hole the smaller the curvature at the horizon. But as the black hole evaporates the horizon moves inwards and the curvature increases. Its at this point when the radius of the black hole reaches the Planck scale that quantum effects will modify the semi-classical picture.

If AS is correct then when the radius reaches the Planck scale gravity will weaken sufficiently such that there is no longer a horizon.

 

[marcus]

...
If AS is correct then when the radius reaches the Planck scale gravity will weaken sufficiently such that there is no longer a horizon.

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.

 

[marcus]

In case anyone else is reading, the argument in support of what Finbar says is not at all complicated or special to Bonanno's paper. It is a simple elementary one.
There is growing evidence that a UV fixed point exists for gravity.
One thing this means is there is a small positive number G* such that as the momentum scale k goes to infinity
we have G(k)k² -> G*

That is, the dimensionless form of Newton's constant goes to G*.

In renormalization, only numbers run, only dimensionless parameters. So the physical Newton's constant gets multiplied by k to make it dimensionless, a pure number.

I have to go, will complete this when I get back. But you can work it out easily by yourself.
It means that as k goes to infinity the physical quantity becomes small.

Gravity is "antiscreened" as Bonanno says. Back soon.

 

[Finbar]

As far as I know that's correct, asymptotic darkness most likely needs flat or anti desitter space to be made sense off. The presence of a positive cosmological constant kills most of the technical assumptions and arguments that goes into it, at least that I am aware off (I am not a gravity specialist).

But I think that's true for most things in quantum gravity. The fate of holography, unitarity, causality, the arrow of time and generalized thermodynamics, and the like are a complete mystery in ds space.

Hell, a lot of gravity people believe that no quantum theory of DeSitter space even exists (again on general quantum mechanics grounds).. No obvious observables, possibly a finite hilbert space, problems with entropy and black holes, etc etc

I think if it were true that quantum theory was in consistent with de sitter space I would give up on some of the principles of quantum theory. But I think the problem here is background dependence. String theorists seem obsessed with what spacetime they put there theory in. But this is largely justified for the reasons Haelfix gave.

Marcus, what matters is the asymptotic spacetime not the whole spacetime. You need Asymptotically(as in at spatial infinity) flat space to define the S-matrix. So the presence of matter is neither here nor there.

What is needed ultimately though is some kind of background independent notion of the vacuum.

I think a good starting place to understand these problems is the problem that one cannot define a local energy for the gravitational field. The only energy one can use is the ADM energy which can only be defined at spatial infinity in an asymptotically flat spacetime. All these other problems really stem from this.

 

[Finbar]

In case anyone else is reading, the argument in support of what Finbar says is not at all complicated or special to Bonanno's paper. It is a simple elementary one.

Indeed Bonanno and Reuter's work is at the heart of most of my argument. Its just my laziness not to cite them. Did you watch Bonanno's talk at the perimeter meeting? It was one of the most interesting i think.

 

[marcus]

Indeed Bonanno and Reuter's work is at the heart of most of my argument. Its just my laziness not to cite them. Did you watch Bonanno's talk at the perimeter meeting? It was one of the most interesting i think.

As it happened it was not one of those I watched. I will go back and watch it on your recommendation. I'm interested in having this thread serve the needs of other people who may not have as much background as you do. So I hope to have things spelled out in slightly more detail than necessary. I'll repeat the link to Bonanno's recent survey. And get a link to the video in case other people want to watch.
This is fascinating stuff! I'm glad you brought it up.
Here is the video link:
http://pirsa.org/09110050/
In the flash video I do not get sound until about minute 3:40 into the talk! If you experience this problem, drag the button to around minute 3 or 4 and start watching there.
Here's the link to the paper that you could say goes along with the video of the talk, but covers more. It's a good survey of what Asymptotic Safety means in relation to cosmology.

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

In case anyone else is reading the point Finbar was making about no black holes below a certain mass, that is is around the top of page 18. I mentioned that earlier. With a gravity UV fixed point, if the mass is below critical, no horizon exists.

In case anyone else is reading, the argument in support of what Finbar says is not at all complicated or special to Bonanno's paper. It is a simple elementary one.
There is growing evidence that a UV fixed point exists for gravity.
One thing this means is there is a small positive number G* such that as the momentum scale k goes to infinity
we have G(k)k² -> G*

That is, the dimensionless form of Newton's constant goes to G*.

In renormalization, only numbers run, only dimensionless parameters. So the physical Newton's constant gets multiplied by k² to make it dimensionless, a pure number.
...
It means that as k goes to infinity the physical quantity Newton's constant becomes small.

Gravity is "antiscreened" as Bonanno says.

I guess the arithmetic is obvious here. If anyone has questions please ask. The argument is very robust. Any UV fixed point in the grav. renorm. flow means that Newton G has to become negligible at very short range or at very high cutoff energy.

I think if it were true that quantum theory was inconsistent with de sitter space I would give up on some of the principles of quantum theory. But I think the problem here is background dependence. String theorists seem obsessed with what spacetime they put there theory in...

I think you are right, but it leads to a sloppy way of talking that can confuse people. We all know the observational evidence is for a positive Lambda. Presumably matter will thin out and asymptotically we will be in a deSitter space. deSitter space is a useful idealization and a good approximation both to very early (inflationary) expansion and to the late-time universe. It has become a paradigm that cosmologists often refer to. But on the other hand it is also obvious that we are not IN a deSitter space. We aren't in any particular fixed background geometry .

 

[atyy]

OK, I'm very confused. Is AS really incompatible with Asymptotic Darkness? AD means if you collide two things at high enough energy, you will form a big black hole, so the horizon will be pretty flat and semiclassical. I understand that AS seems to say that black holes will evaporate to a remnant (http://arxiv.org/abs/hep-th/0602159), whereas string theory seems to say black holes will evaporate completely (http://arxiv.org/abs/hep-th/0601001). But isn't that a different issue from AD?

 

[marcus]

OK, I'm very confused. Is AS really incompatible with Asymptotic Darkness? ...

Heh heh. That reminds me. Takes me back a few years. I remember first reading about Asymptotic Darkness in 2003 in this paper by Tom Banks.
Everyone was very upset that summer because of the KKLT paper (with all the vacuua) and Lenny Susskind had started talking about the anthropic landscape (which somehow made all the vacuua OK). And then Tom Banks came out with what seemed quite fascinating ideas, at the time:

http://arxiv.org/abs/hep-th/0306074
A Critique of Pure String Theory: Heterodox Opinions of Diverse Dimensions
T. Banks (SCIPP, U.C. Santa Cruz, Nhetc, Rutgers U.)
82 pages
(Submitted on 9 Jun 2003)
"I present a point of view about what M Theory is and how it is related to the real world, which departs in certain crucial respects from conventional wisdom. I argue against the possibility of a background independent formulation of the theory, or of a Poincare invariant, Supersymmetry violating vacuum state. A fundamental assumption is black hole dominance of high energy physics. Much of this paper is a compilation of things I have said elsewhere. I review a crude argument for the critical exponent connecting the gravitino mass and the cosmological constant, and propose a framework for finding a quantum theory of de Sitter space."

You ask is asymptotic safety (which is a live issue which a lot of people are excited about and working on) is compatible with what Tom Banks used to call "asymptotic darkness"---which I haven't heard much discussed for some years!

Tom Banks is great. Full of ideas, wonderful way with language. I printed out parts of the paper and enjoyed struggling with it. But asymptotic darkness? As Banks says, it is just an assumption.

We have no evidence that physics up near Planck scale is basically the physics of black holes. The idea is not current. We just had an important conference on Planck Scale in July! One of the most influential string theorists in Europe, Hermann Nicolai, gave a talk which I would recommend anybody to watch. Did he talk about "A.D."? No.
Some fortysix people gave papers about their ideas of the physics from here up to Planck. No discussion of A.D. at least that I'm aware of. [EDIT: Atyy says one speaker did discuss Asymptotic Darkness, namely Giddings. But I have my doubts about that. I watched part of the talk and reviewed the slides---don't think he did. We'll see.]

Too much of an assumption. Could well be a critical mass below which you can't have one. Geometry too uncertain, chaotic, perhaps. Heisenberg attention deficit disorder can't hold still long enough to make a Schwarzschild solution? I have to go to supper. Will try to say more later.

 

[MTd2]

If we assume an analogy to the case of the gases at critical point, I'd expect the following situation, if one could somehow draw a critical line representing the point where a horizon forms, in a graph of density vs. radius.

Above the critical line -> outside horizon
Outside the critical line -> inside horizon

Critical point, both situations meet, and it is located at Planck density and Planck size, which is the most extreme point by the way. Matter at that point would tunnel to the lower side. The only way not to violate the extreme is to expand. Perhaps a Planck photon.

Note here that in this reasoning the only way of matter entering in a black hole it is being disassembled to plank scale, and like being digested, and enter there as through that extreme point. I think it is likely that the energy difference of the states between inside and outside will force a fast enough "digestion".

It is interesting to notice that what if instead of a Planck photon, one got the whole universe in there, or a lot of mass. What one would get? A baby universe? A bouncing univese. Because, that critical point also corresponds to (/\,G) point, and so, the IR limit could follow a momentous trajectory that would cause matter to big bang. Or maybe just collapse to the inside of a black hole, until it self digest it.

You see, although the region that allows the passage of matter is short, and greatly favors the flux outside or inside, there is a small probability of it tunnels back through it.

 

[atyy]

We have no evidence that physics up near Planck scale is basically the physics of black holes. The idea is not current. We just had an important conference on Planck Scale in July! One of the most influential string theorists in Europe, Hermann Nicolai, gave a talk which I would recommend anybody to watch. Did he talk about "A.D."? No.
Some thirty-odd people gave papers about their ideas of the physics from here up to Planck. No discussion of A.D. at least that I'm aware of.

Steve Giddings talked about it.
http://www.ift.uni.wroc.pl/~planckscale/movie/index5.html
http://www.ift.uni.wroc.pl/~planckscale/lectures/5-Friday/1-Giddings.pdf

 

[marcus]

Steve Giddings talked about it.
http://www.ift.uni.wroc.pl/~planckscale/movie/index5.html

Giddings talked about "asymptotic darkness"?
I looked through his slides and found no reference to it.
http://www.ift.uni.wroc.pl/~planckscale/lectures/5-Friday/1-Giddings.pdf

My impression is he was calling everything into question---including the idea that classical general relativity applies, and by implication the idea that black holes can form at Planck scale. I listened to some of his talk and it impressed me as an "outsider's" talk, he was saying all our present ideas are probably inadequate. He argued that we will need radically new ideas to understand physics at that scale. It was something of a "lone opposition" voice.

Since Giddings' talk was so disconnected from the rest, I would be reluctant to watch it again. But I did review his slides and saw nothing about "asym. darkness" and no reference to Tom Banks.
If you can point me to a slide, which I somehow missed, please do. Or to some point in the talk where he actually claims or assumes that high-energy physics is dominated by black holes. It would be in sharp contrast to the rest of what I've heard, and interesting to pinpoint.

BTW turns out there were some 46 speakers. I had the number wrong earlier, so I corrected it.

 

[atyy]

Giddings talked about "asymptotic darkness"?
I looked through his slides and found no reference to it.
http://www.ift.uni.wroc.pl/~planckscale/lectures/5-Friday/1-Giddings.pdf

My impression is he was calling everything into question---including the idea that classical general relativity applies, and by implication the idea that black holes can form at Planck scale. I listened to some of his talk and it impressed me as an "outsider's" talk, he was saying all our present ideas are probably inadequate. He argued that we will need radically new ideas to understand physics at that scale. It was something of a "lone opposition" voice.

Since Giddings' talk was so disconnected from the rest, I would be reluctant to watch it again. But I did review his slides and saw nothing about "asym. darkness" and no reference to Tom Banks.
If you can point me to a slide, which I somehow missed, please do. Or to some point in the talk where he actually claims or assumes that high-energy physics is dominated by black holes. It would be in sharp contrast to the rest of what I've heard, and interesting to pinpoint.

BTW turns out there were some 46 speakers. I had the number wrong earlier, so I corrected it.

I was thinking of slide 6 of http://www.ift.uni.wroc.pl/~planckscale/lectures/5-Friday/1-Giddings.pdf , ie. transplanckian collisions produce black holes.

Yes, maybe a lone ranger - but not as much as Markopoulou - I think her work about emergent locality is inspired by similar considerations.

 

[atyy]

Yes, maybe a lone ranger - but not as much as Markopoulou - I think her work about emergent locality is inspired by similar considerations.

I take the first bit back - he's an alpinist!

 

[atyy]

BTW, I'm not sure if I have this right, but I don't think Asymptotic Darkness is Tom Banks's idea - it's the name that was his.

The idea that transplanckian collisions produce black holes can be found eg.

http://arxiv.org/abs/gr-qc/9510063
Structural Issues in Quantum Gravity
Chris Isham
"This has been emphasised recently by several people and goes back to an old remark of Bekenstein: any attempt to place a quantity of energy E in a spatial region with boundary area A—and such that E > √A—will cause a black hole to form, and this puts a natural upper bound on the value of the energy in the region (the argument is summarised nicely in a recent paper by Smolin)."

http://arxiv.org/abs/gr-qc/9508064
The Bekenstein Bound, Topological Quantum Field Theory and Pluralistic Quantum Field Theory
Lee Smolin
"This suggests that, ultimately, a quantum theory of gravity will not be formulated most simply as a theory of fields on a differential manifold representing the idealized-and apparently nonexistent-“points” of space and time. To put this another way, the space of fields-the basic configuration space of classical field theory-has been replaced in the quantum theory by abstract Hilbert spaces. At the same time, ordinary space, in these formulations, remains classical, as it remains the label space for the field observables. This perpetuates the idealization of arbitrarily resolvable space-time points, that the results of string theory, non-perturbative quantum gravity and semiclassical quantum gravity (through the Bekenstein bound) suggest we must give up."

And more recently
http://www.ift.uni.wroc.pl/~planckscale/lectures/5-Friday/1-Giddings.pdf
http://www.damtp.cam.ac.uk/user/tong/string.html

Of course, this is handwavy, and AS is a direction suggested by Wilsonian renormalization, so we shall have to wait and see.

 

[marcus]

I was thinking of slide 6 of http://www.ift.uni.wroc.pl/~planckscale/lectures/5-Friday/1-Giddings.pdf , ie. transplanckian collisions produce black holes.
...

I see now what you were identifying with "asymptotic darkness." But as I see it, he's not proposing a scenario of what will happen at very high energies. He is certainly not claiming to know. I'd say he is trying to impress the other conferees with how little we know, how inadequate our ideas are.

I don't agree with Giddings and I was disappointed---he could have contributed more to the conference. But at least in any case he wasn't trying to sell them Tom Banks old scenario of asymptotic darkness.
Notice in his picture he puts "BH" in quotes.

One can justifiably be skeptical of any scenario about would happen in a hypothetical collision between an electron and positron each with E >> Planck. (much larger than Planck energy). Does anybody nowadays claim to know?

The Planck energy is enough to run an ordinary automobile well over 100 miles. Roughly equivalent to the energy in half a tank of gasoline, if I remember right. You probably know the exact figure, something like 2 billion joules? He's imagining you give each particle that much energy and have the two collide. He says that a successful theory of qg would be able to say what happens, either explain how a collision would be avoided---explain that collision is theoretically impossible---or describe the collision. His message is we don't know, and we don't even have a clue to the right concepts. He sets what I think is an impractically high bar and in effect discourages people from even trying. But I don't think the others paid much attention.

Did you watch the first discussion session? It was led by Nicolai and was generally about quantum theories of gravity and matter---or Planck scale physics. Why needed? What history? Comparison of various research directions and current status. Then audience discussion. Robert Helling was the guy in the audience who made an angry speech where he kept dropping something onto the desk in front of him.

 

[atyy]

I don't agree with Giddings and I was disappointed---he could have contributed more to the conference. But at least in any case he wasn't trying to sell them Tom Banks old scenario of asymptotic darkness.

Did you watch the first discussion session? It was led by Nicolai and was generally about quantum theories of gravity and matter---or Planck scale physics. Why needed? What history? Comparison of various research directions and current status. Then audience discussion. Robert Helling was the guy in the audience who made an angry speech where he kept dropping something onto the desk in front of him.

I don't think the idea originated from Banks - seems to go back to Bekenstein, and you can find it in papers by eg. Isham, Smolin etc. I've put more detail in the post #96.

 

[marcus]

Atyy, thanks for pointing to these papers. I will try to comment.

http://arxiv.org/abs/gr-qc/9510063
Structural Issues in Quantum Gravity
Chris Isham
"This has been emphasised recently by several people and goes back to an old remark of Bekenstein: any attempt to place a quantity of energy E in a spatial region with boundary area A—and such that E > √A—will cause a black hole to form, and this puts a natural upper bound on the value of the energy in the region (the argument is summarised nicely in a recent paper by Smolin)."

http://arxiv.org/abs/gr-qc/9508064
The Bekenstein Bound, Topological Quantum Field Theory and Pluralistic Quantum Field Theory
Lee Smolin
"This suggests that, ultimately, a quantum theory of gravity will not be formulated most simply as a theory of fields on a differential manifold representing the idealized-and apparently nonexistent-“points” of space and time. To put this another way, the space of fields-the basic configuration space of classical field theory-has been replaced in the quantum theory by abstract Hilbert spaces. At the same time, ordinary space, in these formulations, remains classical, as it remains the label space for the field observables. This perpetuates the idealization of arbitrarily resolvable space-time points, that the results of string theory, non-perturbative quantum gravity and semiclassical quantum gravity (through the Bekenstein bound) suggest we must give up."

The Bekenstein bound is discussed here
http://www.scholarpedia.org/article/Bekenstein_bound
Happily enough Bekenstein himself is the curator of the Scholarpedia article about his bound.

The bound is independent of Newton's G. It relates the entropy S in a region to the energy E in the region and to the radius R of a ball containing the region.
S ≤ 2π R E.
Let's imagine we have adjusted units so hbar=c=1 and omit them, though the pedia article puts them in.

We also have a bound on the amount of energy you can pack into a region with radius R without getting a black hole. This is a well-known consequence of the Schwarzschild radius formula which goes back to the work of Karl Schwarzschild in 1916.
Going by what Wikipedia says, it took years for the idea of a black hole to become accepted. There were papers by Oppenheimer (1939) and Finkelstein (1953). Then a 1967 public lecture by Wheeler gave the term "black hole" wide currency.

This bound on the energy inside a finite region does not have an "official" name as far as I know. We could call it the Schwarzschild bound---and this DOES depend on the value of Newton G. This is a bound on the amount of energy you can pack into a region with radius R. It is just a disguised form of the 1916 Schwarzschild radius formula which each of us must have seen countless times.

R_Schw= 2GM/c² or in terms of the equivalent energy
R_Schw= 2GE/c⁴ and then since we set c = 1
R_Schw = 2GE

I'm ignoring any effects of spin and charge, to keep things simple. So here is a bound on the amount of energy you can stuff into a ball with radius R, without forming a Schwarzschld black hole. This bound on the energy is:
E ≤ R/(2G)

But the area of a ball is A = 4π R² , so that R is proportional to sqrt A.
Forgetting some constants like 2 and π we can simply substitute sqrt A for the radius R, and write this as Isham does:
E ≤ sqrt A.

So far that doesn't seem very interesting. Bekenstein and Isham and Smolin and the others are talking about something more subtle, involving entropy and the dimensionality of the Hilbert space of quantum states. Intuitively because the energy in a bounded region is bounded, so also are things like the entropy and information and state space dimensionality bounded as well.

=============
The above is kind of preamble. Maybe now we are getting to something more interesting.

What does this have to do with renormalization of gravity+matter, and in particular with the running of G and Lambda?

Well intuitively, as the cutoff k -> infty we get that G becomes negligible and Lambda gets large. This could actually prevent a black hole from forming!
Remember the "Schwarzschild bound" on the energy in a given finite region depends on G. So if G is running----or more correctly it is the dimensionless number G(k)k² which runs, converges to a finite fixedpoint number G*---this could interfere with the bound in some very high energy regime.

Bonanno seems to be discussing this kind of thing in his most recent paper.
I should apologize if I've been grouchy earlier. I didn't think the avid discussion of "darkness" had much relevance to the main topic (Weinberg's recent talks and work on renormalization of gravity as a way to explain inflation.) But I now see that there is something interesting to discuss here.

Over the years I've seen many physics arguments that depend on this "Schwarzschild bound" on the energy (or mass) inside finite region if collapse is to be avoided. What if that presumed "bound" is weakened? Which arguments are at risk of being compromised?
I'll try to get back to this later.

 

[atyy]

I didn't think the avid discussion of "darkness" had much relevance to the main topic (Weinberg's recent talks and work on renormalization of gravity as a way to explain inflation.) But I now see that there is something interesting to discuss here.

Over the years I've seen many physics arguments that depend on this "Schwarzschild bound" on the energy (or mass) inside finite region if collapse is to be avoided. What if that presumed "bound" is weakened? Which arguments are at risk of being compromised?
I'll try to get back to this later.

OK, here's a real diversion from condensed matter:
http://arxiv.org/abs/0704.3906
Area laws in quantum systems: mutual information and correlations
M.M. Wolf, F. Verstraete, M.B. Hastings, J.I. Cirac

A more serious question:
Weinberg starts with the most general generally covariant action. But Krasnov has an even more general one. What is the difference? I might guess Weinberg has the most general generally covariant *local* action, but is Krasnov's non-local?