BeGroMaS: gravity was renormalizable after all, so why all the fuss?

[tom.stoer]

Why are you so sure string theory is a consistent QG theory?

There is plenty of evidence that varios different approaches within string theory seem to generate similar or mutual consistent or complementary results. So the chance of being internally consistent is high.

Why are you sure it is the only one consistent? Why cannot have other consistent theories?

Of course other consistent theories are possible; string theory does not rule out other theories. The existence of ducks and beavers in Europe does not rule out the existence of Platypi in Australia.

AS gravity with other stuff can render string theory useless as a fundamental theory and it does not need string theory to be consistent, if proven correct.

AS and other approaches to QG are not as ambitious as string theory. String theory aims to unify all known forces based on an underlying unique "structure" with quantum gravity as an epi-phenomenon. AS (LQG, CDT, ...) does not say anything regarding the rest of the SM.

 

[MTd2]

Heh, I questioned Atty. And I was talking about AS with gravity and other stuff together. AS is just a state of a theory not a theory, and it doesn`t need to be only gravity.

 

[Careful]

. Bashing other's people work caused Motl to loose his academic position. I do not care for such behavior.

Motl went much further, he bashes people, not merely work. There is a big distinction between calling the approach of a respected physicist misguided and using the kind of retoric Lubos does. I hope you can appreciate the distinction.

Careful

 

[marcus]

Gravity is renormalizable after all, so why the big fuss?

I think it could be useful to hear what people thought about the FOUR PROBLEMS WITH AS that Weinberg discussed in his Strings 2010 talk
https://mediamatrix.tamu.edu/streams/327756/PHYS_Strings_2010_3-18-10C
If you want to find that section it is between 1/4 and 1/3 of the way on the video timeline.

Or possibly between 1/5 and 1/3.

1. How do you test that in the real world the couplings are, in fact, on the critical surface?
(That sounds like an empirical project. Map the surface numerically, then measure the real world couplings.)

2. Does the truncation converge? Does the action "settle down" as you include higher and higher derivatives?
(He said that Codello Rahmede Saueressig "tested this experimentally" out to 9 terms and found it was settling down. I think he had "experiment" on his mind and that he really meant to say "tested this numerically". For a theorist maybe anything that is not theoretical is experimental--but with massive use of computers there is really a third category. Weinberg reproduced the table of Codello et al results, illustrating convergence.
Hopefully we will see more numerical work along those lines.)

3. How do we use this?
(He described his efforts to use AS to study the early universe and inflation. He described a frustrating tradeoff or dilemma he faced in choosing the cutoff. I think the early universe and possibly the bounce is a place where AS may have to yield the floor to LQG.
LQG has a quantum model of early universe geometry---and one which goes back before the start of expansion. So it is a natural choice to serve the needs of cosmology, if it turns out that AS is not well adapted. It is also eminently testable: if they don't find the expected evidence of a bounce in polarization CMB data that will strongly disfavor Loop.)

So I think that Weinberg's problem #3 is the only real stumbling block. Problems #1 and 2 simply call for empirical and numerical work, which will either tend to confirm or discredit the AS approach depending on how the trial turns out.

4. What about ghosts?
(He gave reasons why "This is not necessarily a serious problem." and cited 2008 or 2009 papers by Niedermeyer and by Benedetti Machado Saueressig. The basic reason he gave was that you don't find zeros because coefficients run with k². It is again a problem to be investigated numerically. And so far the numerical result is "no ghosts".)

 

[Careful]

you are too negative regarding well-established research progrems; they do not only survive because of money, influence and connections ... Look at the first three decades of the last century; nobody (Planck, Einstein, Bohr, ...) was willing to kill the rstablished theories; they all started rather conservative; they always tried hard to "save" the old approaches. They hesitated to start a revolution. I think the situation is rather comparable, except for the major difference that we today have more researches and more candidate theories. They should be investigated carefully.

This discussion is becoming a bit pointless. Look a bit at the timescales, will we? Problems with electromagnetism started to be documented as far as I know around 1880, some 15 years later Planck made his first daring guess and another 10 years later Einstein wrote his nobel prize winning paper. 15 years later non relativistic QM was established fairly rigorously: total time span 40 years. Now, the revolution concerning QFT went in several steps, but lasted roughly from 1930 till 1970, another 40 years. Now the quantum gravity problem started to be researched by I think mainly Dirac in the 1950 ties, total time span until now 60 years and we didn't start the revolution even yet. The point is that nobody is putting money in fundamental research, even Perimeter is rather mainstream, and everybody who denies that is a liar.

There was I time when I was thinking that strings are dead b/c they are not testable.

Sorry to say, that is a pretty bad reason.

Unfortunately most theories of QG are nearly untestable. So killing one theory due to such a reason means killing them all (the same applies to reasons like internal consistency; it is by no means clear whether any of these theories is consistent or not; look t QM: it was definately inconsistent over decades

That is false, non relativistic quantum mechanics was rigorously established around 1925 by Von Neumann. The difference is that quantum theory evolved and every step was tested theoretically as well as experimentally. None of the approaches so far has this kind of trackrecord despite of 60 years of looking.

Careful

 

[Careful]

I believe we do not really disagree, we just approach the role of this forum quite differently.

No we don't really disagree and there are plenty of other people who treat the role of this forum very differently than we both do. It is very simple, everybody has his own past, experience, depth of understanding and so on ... moreover, on top of that, everybody has a different personality. The only thing which I think one cannot do is call one and another crackpots, idiots, cranks and kick under the belt. For the rest, much is permitted. I may think that you think too much like a knitpicking mathematician with lack of real ideas (otherwise you would not be considerate to things which have less than 10 % of working out) and you may have the attitude that someone like me should prove first that he is first class physicist on the Landau scale before he opens his mouth in the way I do. The matter is, these are facts of sociology, ''subjective morality'' and ''ethics'' and as scientists we should be bloody tolerant towards such issues. But again, I disapprove of people bashing too. Science is a cruel business, you love your baby but you must accept it when it gets eaten by the lions.

Careful

 

[marcus]

Gravity is renormalizable after all, so why the big fuss?

marcus,

The situation regarding testability may not be totally hopeless; there are indeed hints regarding big bounce CMB spectra etc. such that some experimental tests may become possible. But the power of these constraints compared to standard experiments e.g. for QM and QED is poor!
...

Tom, in connection with this you might have a look at my post #124. I list and comment on the four "problems" that Weinberg discussed in his talk on AS to Strings 2010. At least two problems lead, in my view, to suggestions for experimental/numerical work.

I don't want to argue against your qualitative judgment that the observational constraints on LQG are weak. Everyone can see the issue differently and must use their own judgment.

For me, I believe what Barrau et al say about the signature of bounce in CMB polarizartion.
Not finding the expected evidence of bounce would, in my view, be a heavy blow to LQG and would seriously discredit the theory.

It might be more correct to say that at present observation could strongly constrain (to the point of annihilation ) but still might offer little constructive guidance. Constraint in a positive sense might be harder to come by.

 

[humanino]

you think too much like a knitpicking mathematician with lack of real ideas (otherwise you would not be considerate to things which have less than 10 % of working out)

It does not logically follow and your suggestion is insulting. You only reinforce my earlier point about different behavior on this forum.

you may have the attitude that someone like me should prove first that he is first class physicist on the Landau scale before he opens his mouth in the way I do.

This is also insulting that you imply I do not care for you argument because I do not know your CV. It is not the case. I will illustrate below

Science is a cruel business, you love your baby but you must accept it when it gets eaten by the lions.

Certainly, but the lion is never a theorist, the lion is always an experimentalist, or a theorist interpreting an experimental result. So the lion Pauli hurt his reputation teeth on babies Uhlenbeck, Kramers, and Goudsmit, or on babies Yang and Mills. Pauli was indeed a "first class physicist" with pretty good mathematical arguments.

 

[Careful]

It does not logically follow and your suggestion is insulting. You only reinforce my earlier point about different behavior on this forum.
This is also insulting that you imply I do not care for you argument because I do not know your CV. It is not the case.

You are easily insulted; clearly you don't live in europe.

I will illustrate belowCertainly, but the lion is never a theorist, the lion is always an experimentalist, or a theorist interpreting an experimental result. So the lion Pauli hurt his reputation teeth on babies Uhlenbeck, Kramers, and Goudsmit, or on babies Yang and Mills. Pauli was indeed a "first class physicist" with pretty good mathematical arguments.

Ah, in case of Yang and Mills, I don't know if he really was wrong there, that might be still an open issue in spite of the succes of the standard model. Recently, people start to suggest that gauge symmetries might be ''emergent'' and actually I think that there is no real strong theoretical reason why we should take gauge symmetry as a fundamental principle of nature. Feynman didn't think too highly of them either, he called them ''partial symmetries'' as far as I remember. Concerning spin, well that was a new idea and Pauli was a bit too conservative here in the beginning, but I don't see how this applies to the context where my arguments are mainly against conservative ideas and pro-new ones.

But Pauli was certainly a great guy, modern physics could use a few of them. He was also far ahead of his time related to some ideas regarding consciousness.

 

[Haelfix]

Do you know of any non-trivial fixed point that was analytically found?

Yes, indeed there are! I already mentioned the one arising from scalar field theory (which was historically what partially led to the invention of the exact renormalization group) in 3d.

There is one in 2+epsilon gravity. There are some arising from conformal field theory and show up in condensed matter physics. The Ising model in 2d is another important one.
Seiberg-Witten theory captures information about the Argyres Douglas fixed point etc etc

A great deal of research has gone into understanding critical behavior in field theories, and the exact renormalization group has been utilized in theory circles for a long time before the gravity program was initiated.

 

[MTd2]

I vaguely remember that many of those you cited were already studied a long time ago by the method of Wetterich equation. I think Marcus may point those out.

 

[marcus]

I vaguely remember that many of those you cited were already studied a long time ago by the method of Wetterich equation. I think Marcus may point those out.

In fact, I don't have anything to add to what Haelfix said just now.

In his talk to Strings 2010, Weinberg gives a brief sketch of the history, which goes back well before Wetterich's contribution (which Weinberg suggests was not a "first" but was anticipated by someone else, whose name he mentions.) There's a lot of history leading up to the current AS effort. Maybe Haelfix can suggest a review article that gives the history, in case anyone is interested.

 

[atyy]

Why are you so sure string theory is a consistent QG theory? Why are you sure it is the only one consistent? Why cannot have other consistent theories?

AS gravity with other stuff can render string theory useless as a fundamental theory and it does not need string theory to be consistent, if proven correct.

I believe string is consistent because so many pieces of mathematics work out. It could still be that I am wrong, but it's about the level of believing that QCD is consistent, despite the Clay prize. The difference with QCD is that the latter has a pretty complete formulation, but strings still has a lot to be worked out.

I did not say that strings is the only consistent theory - I said it is the only consistent theory known to me.

Yes, AS could render strings physically incorrect. What I want to know is, if pure gravity has a non-trivial fixed point, is that consistent with string theory being physically relevant, eg. if we are off the critical surface (ie. suppose AS is physically incorrect, even though it turns out to be a consistent theory of quantum gravity)? Eg. is AdS/CFT mathematically incompatible with a UV fixed point for pure gravity in AdS spaces, or can both possibilities exist mathematically, and experriment has to decide?

Edit: Actually, maybe AS is inconsistent with AS in AdS spaces - if I remember right, the indications so far are that the fixed point, if it exists, seems to be at positive lambda ...

Edit: Percacci put a nice new picture on his AS page http://www.percacci.it/roberto/physics/as/index.html

 

[marcus]

Edit: Actually, maybe AS is inconsistent with AS in AdS spaces - if I remember right, the indications so far are that the fixed point, if it exists, seems to be at positive lambda ...

Edit: Percacci put a nice new picture on his AS page http://www.percacci.it/roberto/physics/as/index.html

Thanks for pointing out the new picture!

You remember right. Every calculation I've seen of the AS fixed point gives a positive cosmological constant Lambda---as if AS likes deSitter better than AdS.

 

[MTd2]

There is one in 2+epsilon gravity. There are some arising from conformal field theory and show up in condensed matter physics. The Ising model in 2d is another important one.

I found it here!

http://www.percacci.it/roberto/physics/as/erge.html

 

[Finbar]

I think it would be useful if i clarify what is ment by renormalizable/non-renormalizable in different contexts. In a broad sense renormalizable means that within some framework a theory gives both finite values for observables and that only a finite number of experiments must be preformed before we fix all the predictions of the theory.

The original sense in which renormalizablity was used was within perturbation theory such that finite predictions were given order by order in perturbation theory. This was shown by Sin-Itiro Tomonaga, Julian Schwinger and Richard Feynman to be true for QED. The modern name for this sense of renormalization is "perturbativly renormalizable" or "power counting renormalizable".

A consequence of renormalization for any interacting field theory is that the coupling constants depend on the energy scale at which the theory is probed. In QED for example the coupling grows with energy. This means that at some energy perturbation theory must breakdown since the coupling becomes order one. In fact Lev Landau showed the coupling in QED has a pole at a finite energy. What this means more generally is that perturbative renormalization is not a good indication of a theories consistency. What we really want is a theory which gives finite values of observables on all scales.



What one requires for a theory to be "non-pertubativly renormalizable" is that there exists a fixed point in the renormalisation group flow of the theory such that the couplings g_i go to some constant values g_i* as the energy scale is taken to infinity. This is not true of QED. The only consistent theory of QED is a non-interacting theory; theories of this type are said to suffer from triviality.

So although QED is power-counting renormalizable at low energies it is not non-perturbativly renormalizable. As such we should treat QED as an effective QFT valid only up to some finite energy scale.


QCD on the other hand is non-perturbativly renormalizable! This is due to a fixed point at vanishing coupling. This means that at high energies the theory becomes free where as at low energies the coupling grows and the theory becomes strongly coupled. Such a theory is said to be "asymptotically free". As such QCD is a consistent theory at all scales.



Now what of gravity? Well gravity is perturbativly/power-counting non-renormalizable. This would seem to suggest that gravity was a sick theory. However, if we took this as a sign that gravity was "sick" we would also of concluded that QED was a "well" theory, which we know is not the case. The real test is whether gravity has a fixed point in its renormalisation group flow. The problem with gravity is that it contains a coupling with negative mass dimension. This means that the effective dimensionless coupling grows with energy scale. As such gravity is not asymptotically free. However this leaves the possibility that gravity has a fixed point at a non-vanishing coupling. A theory with this property is said to be asymptotically safe.

 

[marcus]

I think it would be useful if i clarify what is ment by renormalizable/non-renormalizable in different contexts. In a broad sense renormalizable means that within some framework a theory gives both finite values for observables and that only a finite number of experiments must be preformed before we fix all the predictions of the theory.

...

What one requires for a theory to be "non-pertubativly renormalizable" is that there exists a fixed point in the renormalisation group flow of the theory such that the couplings g_i go to some constant values g_i* as the energy scale is taken to infinity.

Yes! Thanks for clarifying this issue and making this point. And also one must require that the critical surface be finite dimensional. Having a finite dimensional part of theory space which is carried to fixed point by the flow is what ensures what you said about only a finite number of experiments must be performed.

Only a finite number of parameters must be determined by experiment and then, when they are plugged in, the theory is predictive.

Essentially because once you are on the attractive critical surface you are "safe"---the flow homes in on the UV fixed point.

So that finite dimensionality is the second A.S. condition that is always mentioned.

... However this leaves the possibility that gravity has a fixed point at a non-vanishing coupling. A theory with this property is said to be asymptotically safe.

Right, with that finitedimensionality proviso.

 

[marcus]

Finbar, you might like to know of a nice recent development in AsymSafe gravity. Martin Reuter's new paper:
http://arxiv.org/abs/1012.4280
Renormalization Group Flow of the Holst Action
J.-E. Daum, M.Reuter
(Submitted on 20 Dec 2010)
The renormalization group (RG) properties of quantum gravity are explored, using the vielbein and the spin connection as the fundamental field variables. The scale dependent effective action is required to be invariant both under space time diffeomorphisms and local frame rotations. The nonperturbative RG equation is solved explicitly on the truncated theory space defined by a three parameter family of Holst-type actions which involve a running Immirzi parameter. We find evidence for the existence of an asymptotically safe fundamental theory, probably inequivalent to metric quantum gravity constructed in the same way.
Comments: 11 pages, 3 figures

You know the Holst Action is the basis of LQG. The Holst Action has the Immirzi parameter.
John Baez TWF 280 has a good introductory discussion of this, towards the end.

Well AsymSafe has never had the Immirzi parameter in it! Until now. Reuter is a major AS figure and he has always done AS with metric GR, not with Holst and connection variable and cotetrad. Now finally Reuter has presented a version of AS which is more compatible with LQG. It even has a running Immirzi!

 

[atyy]

Quick note on marcus's post: Niedermeier and Reuter stated explicitly a few years ago in their Living Reviews article that AS can and should be investigated with different classes of actions, and that the existence of AS of any particular class would not be equivalent to AS in another class. So they've probably long been wanting to try this out. I find it amazing that the new paper suggests that a fixed point, if it exists, might be at negative lambda.

@marcus: so are we tilting towards KKL now? AS really is a view of gravity that says the 4D spacetime manifold exists. KKL are the LQG camp that proposes the same (though Rovelli has tried to undo it).

 

[marcus]

...
@marcus: so are we tilting towards KKL now? AS really is a view of gravity that says the 4D spacetime manifold exists. KKL are the LQG camp that proposes the same (though Rovelli has tried to undo it).

Good question Atyy! However I am not good on the day-to-day tilting or the camps
You may not realize how much I rely on you for spotting and reporting significant detail.
Your interpretation of detail often differs from mine but you have a sharp eye for it.

As I indicated, I can't say much about tilting thisway or thatway. I don't think the "4D spacetime manifold exists" issue is at all important in the long run, so apparent tilting around that issue wouldn't matter.

what is so interesting is that Reuter is reaching out in Rovelli's direction--in the general direction of LQG, by doing the Holst version of AS. That could have longterm significance.

Over the past several years I have seen a big multifaceted convergence of approaches in LQG. Compared with what we see now, the Hamiltonian and the Spinfoam approaches used to be miles apart. Spinfoam didn't even have an Immirzi parameter! Now it does, and it looks like AsymSafe Reuter approach could too.

Lewandowski's gambit ("spinfoam for all LQG", the KKL paper) is another case. All this convergence was, I think, in the cards. One was just working with simpler spinfoams to get started---one knew eventually they would be generalized to higher valence vertex, and then a paper like Ding Han Rovelli would complete the process by generalizing to higher valence node in the boundary spinnetwork.

And you know Einstein's disavowal of the physical existence of the 4D manifold. GR itself does not require the manifold to physically exist. Geometry, in GR, is an equivalence class of metrics, not a particular metric on a particular manifold. Make of it what you will we don't have to agree/indeed we probably shouldn't agree. I don't want to convince you of this but I'll say that a manifoldless version of QG is in the cards, in my view, and even Reuter doesn't really need a spacetime manifold to exist. It is just a scratchpad for calculation. Tear it off and throw it away when you are done. So the existence issue is not a big obstacle to anything, in my humble opinion.

there are a lot of thornier problems to be worked out

 

[tom.stoer]

KKL are the LQG camp that proposes the same (though Rovelli has tried to undo it).

The problem with LQG is that the Barbero-Immirzi parameter and the cosmological constant are treated differently than all other couplings

 

[atyy]

The problem with LQG is that the Barbero-Immirzi parameter and the cosmological constant are treated differently than all other couplings

What do you make of stuff like http://arxiv.org/abs/0903.4407 ?

This seems to me a step even further from the AS heuristic, but I find it intriguing.

 

[tom.stoer]

I totally forgot about these BI-field ideas. Yeah, the BI-parameter may become an "ordinary" field and the AS program needs to be adjusted accordingly (applied to the Holst action / Nieh-Yan invariant based on Ashtekar variables). Nevertheless the cc as a quantum deformation SU_q(2) or something like that does not fit to the AS program.

 

[atyy]

I'm not terribly keen on the cc as q-deformation. It seems a lot to take care of an IR divergence, which is probably not a problem in the first place. I would like to see the "UV-like" divergence taken care of, perhaps through Rivasseau's GFT renormalization programme.

 

[erkokite]

Kinda new paper here (2 mos. old). BFL Ward uses his resummation approach, which is similar to and consistent with asymptotic safety to derive a value for the cosmological constant which is close to the observational value (2.4e-3 eV vs 2.368e-3 eV).

Planck Scale Cosmology and Asymptotic Safety in
Resummed Quantum Gravity

In Weinberg’s asymptotic safety approach, a finite dimensional critical surface for a UV stable
fixed point generates a theory of quantum gravity with a finite number of physical parameters. We argue that, in an extension of Feynman’s original formulation of the theory, we recover this fixed-point UV behavior from an exact re-arrangement of the respective perturbative series. Our results are consistent with the exact field space Wilsonian renormalization group results of Reuter et al. and with recent Hopf- algebraic Dyson-Schwinger renormalization theory results of Kreimer. We obtain the first "first principles" predictions of the dimensionless gravitational and cosmological constants and our results support the Planck scale cosmology of Bonanno and Reuter. We conclude with an estimate for the currently observed value of the cosmological constant

http://arxiv.org/PS_cache/arxiv/pdf/1012/1012.2680v1.pdf"

I'm not 100% sure of the exact link between Ward's work and the AS approach, but it seems to be this- Ward has found that a generalized YFS resummation of the perturbative expansion in Feynman's formulation of quantum gravity which is claimed to produce a perturbatively renormalizable and UV complete formulation of QG which also results in a fixed point. It seems to me that Ward's approach is probably equivalent to the RG picture, but he has found a resummation that produces consistent results as opposed to using the RG directly.

 

[marcus]

BFL Ward's paper was on our poll (about the relative interest/importance of QG papers that appeared in the last 3 months, Oct-Dec 2010.)

https://www.physicsforums.com/showthread.php?t=458853

Check it out. It is a multichoice poll so you can vote for several, and the poll is public, so if you click "results" and then on the number of votes a paper got, you can see who selected it.
It's still open, so anyone who hasn't registered their picks can do so.

 

[arivero]

Ward has found that a generalized YFS resummation of the perturbative expansion in Feynman's formulation of quantum gravity which is claimed to produce a perturbatively renormalizable and UV complete formulation of QG which

Do they sum order by order, or all the series? I mean, there are two structures of divergences in perturbative QCD: the divergences at a given order of the coupling, and the divergence of the renormalised series itself.

 

[murray92]

Do they sum order by order, or all the series? I mean, there are two structures of divergences in perturbative QCD: the divergences at a given order of the coupling, and the divergence of the renormalised series itself.

Maybe you want to watch the talk he gave at the asym conferenze last year.
http://www.perimeterinstitute.ca/Events/Asymptotic_Safety/Abstracts/#ward

I think he also gave one at ICHEP in Paris this year about his resummed Quantum Gravity

 

[A. Neumaier]

Maybe you want to watch the talk he gave at the asym conferenze last year.
http://www.perimeterinstitute.ca/Events/Asymptotic_Safety/Abstracts/#ward

I think he also gave one at ICHEP in Paris this year about his resummed Quantum Gravity

See also
http://arxiv.org/pdf/hep-ph/0610232 (published as: Int.J.Mod.Phys.D17:627-633,2008),
and more recently arXiv:1008.1046, arXiv:0908.1764.