# I'm excited about Martin Reuter's Loops '07 talk, comments on it?

1. Jul 28, 2007

### marcus

Alejandro Satz blog has comment on Reuter's Loops '07 talk
Also several people have remarked about what Reuter had to say in his lectures at the Zakopane QG school earlier this year. It made a big impression on the grad students there.

I have listened to his Loops '07 talk several times while scrolling through the slides and I'm seriously interested. I'd really like to hear other people's comments on it.

Reuter gave invited plenary talks at Loops '05 and Loops '07 (there was no conference in 2006) and lectured at the Zakopane school.
2005 plenaries:
http://loops05.aei.mpg.de/index_files/Programme.html
2007 plenaries:
http://www.matmor.unam.mx/eventos/loops07/plen_abs.html
first QG Network school:
http://www.fuw.edu.pl/~kostecki/school.html

The above talks are recorded and available online. In particular here are the Loops '07 talks:

slides:
http://www.matmor.unam.mx/eventos/loops07/talks/PL3/Reuter.pdf

audio:
http://www.matmor.unam.mx/eventos/loops07/talks/PL3/Reuter.mp3

=================

In case anyone wants to see a sample of Reuter's past research papers, just out of curiosity, here are some of the more widely cited ones.

FIND A REUTER, MARTIN AND AFF DESY AND TOPCITE 50+
http://www.slac.stanford.edu/spires/find/hep/www?rawcmd=FIND+A+REUTER%2C+MARTIN+AND+AFF+DESY++and+Topcite+50%2B&FORMAT=www&SEQUENCE=citecount%28d%29 [Broken]
FIND A REUTER, MARTIN AND AFF CERN AND TOPCITE 50+
http://www.slac.stanford.edu/spires/find/hep/www?rawcmd=FIND+A+REUTER%2C+MARTIN+AND+aff+CERn+AND+TOPCITE+50%2B&FORMAT=www&SEQUENCE=citecount%28d%29 [Broken]
FIND A REUTER, MARTIN AND AFF MAINZ U., INST. PHYS. AND TOPCITE 50+
http://www.slac.stanford.edu/spires/find/hep/www?rawcmd=FIND+A+REUTER%2C+MARTIN+AND+AFF+MAINZ+U.%2C+INST.+PHYS.+AND+TOPCITE+50%2B&FORMAT=www&SEQUENCE=citecount%28d%29 [Broken]
FIND A REUTER, MARTIN AND AFF HANNOVER U. AND TOPCITE 50+

====================
Alejandro Satz blog comment on Reuter's presentation is here:
http://realityconditions.blogspot.com/2007/07/loops-07-conference-report-part-2.html

Last edited by a moderator: May 3, 2017
2. Jul 28, 2007

### marcus

Einstein-Hilbert action is a PREDICTION of the theory

I've noticed that many people think that in all the non-string QG approaches one starts by putting in the Einstein-Hilbert action by hand. this was not my impression---maybe with some yes and with some no. In this case it is a very clear no. He doesnt tell the theory he wants the particular action of GR---he tells it certain requirements like diffeomorphism invariance and that the degrees of freedom should be given by the metric tensor g.

What the theory predicts, as a RenormGroupFlow fixed-point, turns out to be the Einst. Hilb action plus quantum corrections.

Some of the success of Reuter approach is due to the fact that he happened to SUCCEED at doing something Steven Weinberg tried to do in 1979, and failed.

See page 5. Weinberg succeeded for lower dimension, like e.g. 2D, but couldnt make it work for 4D. If he had succeeded then Weinberg would have quantized Gen Rel simply and directly in a familiar way used in ordinary quantum field theory. So then we would not be thinking of quantizing GR as being obstructed by non-renormalizability.
Weinberg's program of Assymptotic Safety failed in 1979, but Reuter appears to have got it to work starting in 1996. He and coworkers have been checking and rechecking to make sure for the past ten years.

He calls it QEG (quantum einstein gravity) because it is a direct, no-frills, quantization of general relativity more or less as Einstein wrote it, with the metric tensor as the main variable.

See page 12. Background independence. Also no special action plays a distinguished role.

See page 16. He gets inflation in the early universe without needing an "inflaton" field.

Page 28. possible mechanism to explain the observed structure formation in early universe----the observed spectrum of fluctuations

Last edited: Jul 28, 2007
3. Jul 29, 2007

### Chronos

It is a brilliant piece of work, IMO, marcus. I'm very surprised it has not garnered more attention. But, QG abounds with new ideas this year. I suspect Reuter's work will gain traction next year.

4. Jul 29, 2007

### Careful

I've noticed that many people think that in all the non-string QG approaches one starts by putting in the Einstein-Hilbert action by hand. this was not my impression---maybe with some yes and with some no. In this case it is a very clear no. He doesnt tell the theory he wants the particular action of GR---he tells it certain requirements like diffeomorphism invariance and that the degrees of freedom should be given by the metric tensor g. ''

Marcus, if you are working with a metric theory which is diffeomorphism invariant, then Einstein Gravity pops out just like that because it is the *unique* second order metric - diff invariant theory. The higher order curvature terms are then to be considered as corrections (this was basically known before World war 2 I guess).

5. Jul 29, 2007

### f-h

Yep Einstein-Hilbert action plus cosmological constant and higher R terms is a direct result of the assumptions. In fact what they do in their truncation approximation is assume that the action has the form of a polynomial of order 6 in the curvature.

Careful, out of curiosity do you know any place where a good prove of that is written down? I can see how the hand wavy argument would go, but you know any place where its spelled out in detail?

6. Jul 29, 2007

### Careful

I am not sure anymore (it has been a while) but it might be that if not an argument - a reference to a full blown proof - can be found in the book of Weinberg.

7. Jul 29, 2007

### marcus

I will try to get some publication/citation data on Reuter, particularly as an important figure in Quantum Cosmology. Since 1996 (when he posted a seminal paper)
http://www.citebase.org/abstract?id=oai:arXiv.org:hep-th/9605030 [Broken]
many of his publications have been all or partly devoted to bringing out the cosmological implications of his Asmptotically safe QG picture.

The 1996 seed paper now has about 120 citations---more or less depending on which source you consult. It is currently getting about 3 cites a month---that is on average every month three new research papers come out which refer to it.

It is actually a good introduction to the subject and clearly written, so I will copy the abstract here. It supplements the Loops '07 talk and even though 10 years prior the notation is largely the same, so it can help fill in detail for the talk.

http://arxiv.org/abs/hep-th/9605030
Nonperturbative Evolution Equation for Quantum Gravity
Martin Reuter
35 pages. Phys.Rev. D57 (1998) 971-985
(Submitted on 6 May 1996)

"A scale--dependent effective action for gravity is introduced and an exact nonperturbative evolution equation is derived which governs its renormalization group flow. It is invariant under general coordinate transformations and satisfies modified BRS Ward--Identities. The evolution equation is solved for a simple truncation of the space of actions. In 2+epsilon dimensions, nonperturbative corrections to the beta--function of Newton's constant are derived and its dependence on the cosmological constant is investigated. In 4 dimensions, Einstein gravity is found to be 'antiscreening', i.e., Newton's constant increases at large distances."

Last edited by a moderator: May 3, 2017
8. Aug 17, 2007

### marcus

http://arxiv.org/abs/0705.1769
Ultraviolet properties of f(R)-Gravity
Alessandro Codello, Roberto Percacci, Christoph Rahmede
4 pages
(Submitted on 12 May 2007)

"We discuss the existence and properties of a nontrivial fixed point in f(R)-gravity, where f is a polynomial of order up to six. Within this seven-parameter class of theories, the fixed point has three ultraviolet-attractive and four ultraviolet-repulsive directions; this brings further support to the hypothesis that gravity is nonperturbatively renormalizable."

IMHO the paper is a gem.

Last edited: Aug 17, 2007
9. Aug 18, 2007

### Chronos

Agreed, marcus. I am waiting for the community to dissect this work. Reuter makes a few bold assertions, but his results are undeniably important. Is the metric tensor fundamental? Is the Immirizi paramenter fundamental? Is the BR interpretation fundamental? Perhaps. I like this approach. It piques my interest.

10. Aug 18, 2007

### jal

http://arxiv.org/PS_cache/arxiv/pdf/0705/0705.1769v1.pdf
It can be shown in general that if a gravitational FP exists, Newton’s constant will have an anomalous dimension equal to two [10],

In this letter we present for the first time evidence that in pure gravity the UV critical surface is finite dimensional.

The most important new result of our calculation is that in all truncations the operators from R3 upwards are irrelevant.

With a finite dimensional critical surface, one can make definite predictions in quantum gravity.
--------------
Could someone give me their interpretation and the implication on strings and extra dimensions ?

11. Aug 18, 2007

### marcus

Hi Jal, you ask about several things, all are tied to the Codello Percacci Rahmede paper (IMO a very good paper) that you cite and quote.

"anomalous scaling dimension" doesnt mean "string theory extra dimension". It is a technical thing that occurs (among other places) in ancient ( 1950s) renormalization biz----you know that different physical quantities scale differently with length (area, volume, mass, energy, etc ) some go as the square, some as the cube, some as the reciprocal...
But sometimes in extreme situations things might scale UNEXPECTEDLY.
Like as you make something smaller length you expect its area to decrease as the square of length, but maybe because of bumpiness a correction term creeps in for extreme small lengths and this correction does NOT go as the square.
that's a toy example, but maybe you get the idea. SCALING DIMENSION has to do with practical calculations of physical quantities and how they scale relative to each other, and anomalous has to do with unexpected or unclassical deviations.
the main thing is THIS IS NOT AN IMPORTANT POINT IN THE PAPER. So it is not something to let your attention get hung up on.
All they are doing with that particular mention is giving a plausibility argument for why consider POLYNOMIAL f(R) containing HIGHER ORDERS OF THE CURVATURE.

that is the whole game they are playing. a THEORY is given by its ACTION FUNCTIONAL ("least action principle") and the standard action functional (
einst-hilb) is simply LINEAR in the curvature----so you play the game of adding possible correction terms, one in the square, one in the cube etc etc.
and they go all the way up to a polynomical of POWER SIX in the curvature.

so they have 7 coefficients to play with, counting the constant term of the polynomial. and they want to see if allowing that extra freedom makes any difference. Maybe the RG flow will go in that direction or maybe it will stay happy with just, say, three non-zero terms.

John baez has some background on Renormalization
http://math.ucr.edu/home/baez/renormalization.html
there is also a Wikipedia about renormalization
there is even a Wikepedia about "anomalous scaling dimension", but that is not something to worry about at this point---just a computational detail.
===========THE OTHER THREE THINGS=============
BOTTOM OF PAGE 2
In this letter we present for the first time evidence that in pure gravity the UV critical surface is finite dimensional.

TOP OF PAGE 4, left column and right column
The most important new result of our calculation is that in all truncations the operators from R3 upwards are irrelevant.

With a finite dimensional critical surface, one can make definite predictions in quantum gravity.

these all say the same thing. they took a 7 dimensional theory space (made of all the different actions they could cook up by varying those 7 coefficients)
and they found the fixed point, where the flow wants to go.

and they found that there was a CRITICAL HYPERSURFACE of points in theory space where if you are there the flow sucks you in towards the fixed point.

but if you have a nonzero number for any of the other four, off the hypersurface, the flow blows you away. so those HAVE TO BE SET TO ZERO.

those four are called "irrelevant"

the idea is that the SPACE OF ALL POSSIBLE ACTION FUNCTIONAL COULD BE INFINITE BECAUSE you could have a polynomial with arbitrary high powers of the Ricci scalar R, you could have an infinit long polynomial. So we GIVE NATURE A CHANCE TO LIKE DEGREE SIX, AND SHE DOESNT. The space of action functionals looks like it WANTS TO BE THREE DEE. because if you give the flow a chance to work with higher order terms it just says Yuck and blows them away and says "irrelevant".

What they found was that the space of functionals might as well be cut down to that 3D hypersurface.

That is why they say
The most important new result of our calculation is that in all truncations the operators from R3 upwards are irrelevant.

and that is also why they say you can make PREDICTIONS because you can EXPERIMENTALLY MEASURE the three numbers that matter (say in our everyday classical regime) and then use the flow to run them into extreme territory (like the big bang or a black hole) and use those new numbers to make predictions. And maybe then be able to CHECK then.

One thing it already does is predict inflation-with-graceful-exit just by the running of Lambda.
(no exotic inflaton field needed to drive it, no "slow-roll" fantasy needed to shut it off---the RG flow provides exactly the right amount and then stops)
Something it "post-dicts" is the entropy of the Cosmic Microwave Background. (that's in the Bonanno Reuter paper)
Those things come from taking the classic measured values of G and Lambda in our everyday world and running by the RG.

So what this little 4page paper by Codello Percacci Rahmede does is it confirms or gives evidence that kind of prediction is valid.

I think CODA means "tail" and so codello would mean "little tail", and
percacci would be pronounced PER KA CHEE

the number of players on the Asymptotic Safe field is growing so we have to learn more names.
===================

I gave you my interpretation. As for the other I think string/extradimension more or less irrelevant----not very interesting in this context.

Last edited: Aug 18, 2007
12. Aug 18, 2007

### jal

Thanks marcus!
I think that I had it pretty close.... not as well explained ... I don't consider your explanation as "talking down" to me. Readers who are experts in other areas also need this kind of basic explanation.
I was familiar with J. Baez's explanations. (could be helpfull for others)
I did not want to start a fight with strings/extra dimensions people but both of those approaches cannot be 100% right.
EDIT
hehehe My keyboard just locked up... had to shut down and restart heheh.....didn't want me to ask/cause more trouble.
This seems important. Gravity ONLY 2d

jal

Last edited: Aug 18, 2007
13. Aug 19, 2007

### Chronos

This is a 3d version of gravity - a very important result. You are missing the big picture here I think, jal.

14. Aug 19, 2007

### jal

Chronos
Darn.... I should never listen to what nobel prize winners say.
------------
http://arxiv.org/PS_cache/gr-qc/pdf/9310/9310026v1.pdf
DIMENSIONAL REDUCTION in QUANTUM GRAVITY†
G. ’t Hooft
19 Oct 1993
Abstract
The requirement that physical phenomena associated with gravitational collapse
should be duly reconciled with the postulates of quantum mechanics implies that at a Planckian scale our world is not 3+1 dimensional. Rather, the observable degrees of freedom can best be described as if they were Boolean variables defined on a two-dimensional lattice, evolving with time. This observation, deduced from not much more than unitarity, entropy and counting arguments, implies severe restrictions on possible models of quantum gravity. Using cellular automata as an example it is argued that this dimensional reduction implies more constraints than the freedom we have in constructing models. This is the main reason why so-far no completely consistent mathematical models of quantum black holes have been found.
------------
jal

15. Aug 19, 2007

### marcus

hats off to you, Jal.
if it ever sounds to you like I am "talking down", you are welcome to let me know (PM or public) especially if it interferes with communication

one reason I simplify is I am talking to myself and I try to translate everything I can into simple language because the process of translating
usually helps me understand it better.

the 't Hooft paper seems to be an interesting find. I havent looked at it yet, but it is striking how there is this threeway convergence between 't Hooft, and then Reuter (by an entirely different route) and then Renate Loll (who is also at Utrecht in 't Hooft's institute) using a COMPUTER MODEL of monte carlo random universes that self-assemble out of simplex lego-blocks.

'tHooft says it apparently because of general philosophical reasons
and Reuter says it because he uses mathematical ANALYSIS to renormalize gravity and then it comes out unexpectedly
and then Loll finds it also unexpectedly in a NUMBERCRUNCH numerical simulation with legoblocks of spacetime.

Philosophical, analytical, and brute numerical methods are inherently very different.

BTW you could say I'm talking down because this is all obvious, but actually it is a kind of thinking (I'm talking to myself). Really amazing coincidence.
And Reuter says that Alain Connes has shown some interest.

Last edited: Aug 19, 2007
16. Aug 19, 2007

### jal

I like to read Ph.D. Thesis because they are (I assume) making a summary and an explanation of the present state of the subject. (AND of course, not making “waves” with their personal point of view). It is a “talk down” demonstration of their understanding of the subject.
For example http://arxiv.org/PS_cache/gr-qc/pdf/0609/0609011v1.pdf
The Cosmological Constant Problem, an Inspiration for New Physics
Stefan Nobbenhuis
Ph.D. Thesis, defended June 15. 2006
Supervisor: Prof. Dr. G. ’t Hooft.

p.9
“If one believes quantum field theory to be correct all the way up to the Planck scale, at 1019 GeV, then this scale provides a natural ultraviolet cutoff to all field theory processes like eqn. (1.1). Such a cutoff however, would lead to a vacuum energy density of (1019 GeV)4 = 1076 GeV4, which is roughly 123 orders of magnitude larger than the currently observed value:”
“Even a cutoff at for example the QCD scale (at ∼ 200 MeV), worrying only about zero-point energies in quantum chromodynamics, would not help much; such a cutoff would still lead to a discrepancy of about 40 orders of magnitude.
The answer clearly has to lie somewhere else. Even non-perturbative effects, like ordinary QCD instantons, would give far too large a contribution if not cancelled by some fundamental mechanism.
4This often mentioned factor ∼ 120, depends on the dimension used for energy density. In Planckian units,
the factor 120 is the correct one, relating dimensionless numbers.

(QCD, 10^-18 is my cut off and I’m proposing a fundamental mechanism – minimum length with the dynamical resulting structure. A continuation of G. ’t Hooft’s ideas )
p.10
“As a nice example, Pauli in the early 1920’s was way ahead of his time when he wondered about the gravitational effect of the zero-point energy of the radiation field. He used a cutoff for the radiation field at the classical electron radius and realized that the entire universe “could not even reach to the moon” [4]. The calculation is straightforward and also restated in [5].”
p.11
“All we know for certain is that the unification of quantum field theory and gravity cannot be straightforward, that there is some important concept still missing from our understanding. Note that the divergences in the cosmological constant problem are even more severe than in the case of the Higgs mass: The main divergences here are quartic, instead of quadratic. It is clear that the cosmological constant problem is one of the major obstacles for quantum gravity and cosmology to further progress.”
---------------
So…. That is why I’m interested in “scaling” and “dimensional reduction.” Maybe someone will find the answers to get further progress by this method.
Jal
ps. I’m not “talking down” either. I’m trying to pass on info to readers who are experts of something else.
jal

17. Aug 19, 2007

### jimgraber

on 2D and 3D in gravitation: In Hawking's theory, the entropy of a black hole is proportional to its area, not its volume. This is sometimes called Holography and there is an enormous literature about it. It is not clear to me how (or if) this relates to the three ideas Marcus mentions.
Best,
Jim Graber

18. Aug 20, 2007

### Chronos

A black hole cannot, by definition, have a volume - only a surface. Hawking made a profoundly logical assertion on this count. Spacetime, along with the concept of volume, ceases to exist inside the event horizon.

Last edited: Aug 20, 2007
19. Aug 20, 2007

### marcus

I don't agree with that, Chronos,

I think there is an OK spacetime inside the horizon. It is just a different geometry from usual.

I think the concept of volume makes sense inside the horizon because there is a metric that lets you calculate the volumes of small things. Like coffee mugs and thermos jugs.

think of a supermassive black hole of the sort that are seen in the cores of galaxies----like a billion solar mass----so the radius is a couple billion miles.

imagine dropping stuff in---like souvenir coffee mugs and old television sets---and some lawyers to go along and observe.

I can't picture the stuff losing its well-defined volume immediately upon crossing the horizon into the interior.

I am not saying that it makes sense to talk about the volume of the entire space inside the event horizon including the classical singularity----that's different. In classical GR any region containing the singularity might be infinite, the volume might not compute.
But I don't expect the volume of small objects to immediately stop being well-defined. Am I missing something? Would you like to explain?

http://cosmology.berkeley.edu/Education/BHfaq.html

Last edited: Aug 20, 2007
20. Aug 20, 2007

### topovrs

You are right in saying that volume remains well defined within the local region of any observer who has crossed the event horizon. But the extent of the (interior) region that can be mapped by the observer will be limited.

The event horizon is a lightlike surface, and the radial direction inside a blackhole, in the usual coordinate system, is timelike. All light rays emitted by the observer converge on the singularity without encircling it. So any spacelike 3-volume inside the event horizon must be confined to less than 4 pi of solid angle. Defining the total interior volume of a black hole is thus not possible.

topovrs