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

[PAllen]

We do. String theory. In particular, AdS/CFT, which unfortuantely has already been falsified. But maybe studying it will give us some ideas. And maybe the rest of string theory will also turn out to be coherent.

Hey, can you tell me about this? I thought this was a significant achievement of the string program, and never heard it was in doubt.

Thanks.

 

[atyy]

Hey, can you tell me about this? I thought this was a significant achievement of the string program, and never heard it was in doubt.

Thanks.

I mean that although AdS/CFT is almost certainly a coherent theory of quantum gravity, it doesn't seem to give rise to cosmologies that match observations.

 

[tom.stoer]

But isn't the point that in QG, we are looking for all theories that are internally consistent. Consequently, the statement is of course mathematical in nature. Whether the physics is correct is decided by comparison with observations. The Wilson-Weinberg viewpoint is very simple, either it is consistent with a UV fixed point, like QCD, or new degrees of freedom must be introduced, like string theory. There are theories known where the fixed point is non-Gaussian, the only question is whether gravity without additional degrees of freedom is such a theory.

I'll try to come back to the original topic, so this could be a good starting point.

The main problems in QG (including AS approch) seem to be
- renormalizibility
- non-perturbative approach (related)
- background independence

If this can be achieved consistently then one has a theory of QG that is viable theoretically. If the latter can be addressed in the AS approach is still unclear to me; I have to go though all the details.

Now, assume that the above mentioned steps have been completed, then we are in a rather strange situation: we have the interactions SM + QG(AS) valid up to Planck scale (or perhaps beyond), but we know that the SM still has some problems. Perhaps the different interactions influence each other such that e.g. QED becomes soft (asymptotoically free) instead of having a Landau pole. Fine. But the remaining question is about unification (not directly relatated to QG).

The picture then is
- no need for SUSY and strings
- no idea how to bring these interactions together, no common principles

 

[PAllen]

I'll try to come back to the original topic, so this could be a good starting point.

The main problems in QG (including AS approch) seem to be
- renormalizibility
- non-perturbative approach (related)
- background independence

If this can be achieved consistently then one has a theory of QG that is viable theoretically. If the latter can be addressed in the AS approach is still unclear to me; I have to go though all the details.

Now, assume that the above mentioned steps have been completed, then we are in a rather strange situation: we have the interactions SM + QG(AS) valid up to Planck scale (or perhaps beyond), but we know that the SM still has some problems. Perhaps the different interactions influence each other such that e.g. QED becomes soft (asymptotoically free) instead of having a Landau pole. Fine. But the remaining question is about unification (not directly relatated to QG).

The picture then is
- no need for SUSY and strings
- no idea how to bring these interactions together, no common principles

You can use dark matter plus easier unification as a motivation for SUSY orthogonal to QG. This synergy has made me believe in the likelihood of SUSY independent of what happens with the string program.

 

[tom.stoer]

Agreed - but I guess one must face the idea that this is peraps the final truth.

 

[atyy]

Furthermore, can one show that AS remains when whatever matter is added in?

 

[tom.stoer]

Furthermore, can one show that AS remains when whatever matter is added in?

It hasn't been done so far.

This is another problem if you are not able to provide some kind of unified approach: You would have to check for each matter content seperately. So there should be some approach (SUGRA?) which allows you check a whole class of models.

 

[Careful]

If this can be achieved consistently then one has a theory of QG that is viable theoretically. If the latter can be addressed in the AS approach is still unclear to me; I have to go though all the details.

Of course not ! What about all other things like : (a) definition of observers (b) causality (c) locality (d) measurement problem and so on... All you have done when you solve the problems you adress is constructed a mathematical devise which allows you to compute some scattering matrix between asymptotic observers, there are no observations within the universe, no control over causality (which perturbation theory allows you to do) and so on. I think I once told you, that doing the technical excercise gives you a score of 33%, not 100%.

You see, that's the difference between me and most people, I am actually interested in *physics* and the mathematics is just a tool, not a purpose in itself.

Careful

 

[Careful]

Ever looked at lattice gauge theories? Perhaps you do not care b/c it's conceptually boring - but they can calculate observables :-)

This came only to my mind this morning, but the observables you are talking about are holonmies and field strength's I guess. But then, you never measure those things, how do you define particle in lattice approach given that you break Poincare invariance ? How do you define click of a measurement apparatus ?

 

[humanino]

Thank you Marcus for the link. How do you interpret Witten's question at the end of Weinberg's talk ? He asks whether they find conformal symmetry at the fixed point. Weinberg answers that they certainly have scale invariance, but he cannot tell for the full conformal. My interpretation is that full conformal is necessary for consistency with string theory. Horava also comments in that sense during the next talk.

 

[tom.stoer]

What about all other things like : (a) definition of observers (b) causality (c) locality (d) measurement problem and so on... All you have done when you solve the problems you adress is constructed a mathematical devise which allows you to compute some scattering matrix between asymptotic observers, there are no observations within the universe, no control over causality (which perturbation theory allows you to do) and so on.

You are too much focussed on old-fashioned QM, measurement problem, perturbative particle physics etc.

(a+d) have to be eliminated, not "solved"; I think that a holographic approach where quantum theories and boundary Hilbert spaces are defined on surfaces of observed world volumes is nice
(b) is eliminated if it's background independent (it is only a problem if you have a background according to which the theory shall be causal; that's the wrong approach)
(c) of course; but where do you see indications that it fails to be local?

Of course one has to solve these issues, but most of them are NOT physical. They are technical and belong to old-fashioned thinking based on perturbative particle physics. They are problems created by our methods, not by nature.

 

[tom.stoer]

... but the observables you are talking about are holonmies and field strength's I guess.

Wrong guess :-)

Lattice gauge theory is mostly about expectation values <X> = ∫ DU X exp iS

 

[Careful]

You are too much focussed on old-fashioned QM, measurement problem, perturbative particle physics etc.

(a+d) have to be eliminated, not "solved"; I think that a holographic approach where quantum theories and boundary Hilbert spaces are defined on surfaces of observed world volumes is nice

Of course, they have to be solved, they constitute the map between theory and interpretation. Without realistic interpretation, you have no theory. QFT does not put away these problems either, it restricts it self to asymptotic observers. If you feel this is physically realistic, please take your rocket and move to the boundary of the universe (and we will continue to discuss from thereon ).

(b) is eliminated if it's background independent (it is only a problem if you have a background according to which the theory shall be causal; that's the wrong approach)

Sorry, but you hit the ball entirely wrong here. NOBODY knows what causality means in a BI quantum theory of gravity ! In CDT for example, people have no control over causality whatsoever in contrast what the first letter may suggest to you.

(c) of course; but where do you see indications that it fails to be local?

Non locality is a generic feature of quantum gravity and cannot be restored, unless you modify QM a la 't Hooft.

They are problems created by our methods, not by nature.

Partially true, partially not ; see my first comment.

Careful

 

[Careful]

Wrong guess :-)

Lattice gauge theory is mostly about expectation values <X> = ∫ DU X exp iS

Well, I guess both are correct, Wilsonian observables are often computed in lattice theories. But even then, how do you *measure* such expectation values, what is your theory of measurement and particles ? No answer to that huh, have you ?

 

[tom.stoer]

Well, I guess both are correct, Wilsonian observables are often computed in lattice theories. But even then, how do you *measure* such expectation values, what is your theory of measurement and particles ? No answer to that huh, have you ?

There is no "theory of measurement". That's misguided thinking due to "the measurement problem". One has to overcome this differently; developping a "theory of measurement" within the QM framework is certainly wrong.

But I think that has nothing to do with QG.

 

[MTd2]

Benedetti Groh Machado Saueressig have (what will probably turn out to be) a landmark paper where they show the Renormalization Group Flow treatment of gravity is background independent.

Isn`t it a good reason for a huge fuss? Besides, they come up to a method in which humans are no longer required, just a computer.

 

[Careful]

There is no "theory of measurement". That's misguided thinking due to "the measurement problem". One has to overcome this differently; developping a "theory of measurement" within the QM framework is certainly wrong.

But I think that has nothing to do with QG.

Why do you say such silly things ? There are different measurement problems. The one you are talking about is a slim version of the one I am interested in. All you say is the following:
(a) all I can calulate are correlation functions
(b) I have no procedure for measuring these correlation functions within the universe
(c) all I can do is calculate S-matrix using LSZ type formulae
Therefore, I have no realistic theory of observation.

My conclusion : hence, your theory is wrong since it directly contradicts experience.

End of story; the only one who is misguided here is you.

Careful

 

[marcus]

Here is a Steven Weinberg talk on the topic. It is basically his baby.
https://mediamatrix.tamu.edu/streams/327756/PHYS_Strings_2010_3-18-10C

If anyone tries this link and can't get the video, please let me know. My guess is that Weinberg is pleased with this paper by BGMS. We may hear something about that.

Thank you Marcus for the link. How do you interpret Witten's question at the end of Weinberg's talk ? He asks whether they find conformal symmetry at the fixed point. Weinberg answers that they certainly have scale invariance, but he cannot tell for the full conformal. My interpretation is that full conformal is necessary for consistency with string theory. Horava also comments in that sense during the next talk.

I'm glad you found it interesting! Unfortunately I don't have much useful to add to your interpretation of the question Witten asked, and of Weinberg's answer.
I think the question of scale invariance (and possible conformal symmetry) at the UV fixed point (if it exists) is of general interest. I have seen it raised in other contexts besides string.

Benedetti Groh Machado Saueressig have (what will probably turn out to be) a landmark paper where they show the Renormalization Group Flow treatment of gravity is background independent.
...
http://arxiv.org/abs/1012.3081
The Universal RG Machine
Dario Benedetti, Kai Groh, Pedro F. Machado, Frank Saueressig
38 pages
(Submitted on 14 Dec 2010)
...

Isn`t it a good reason for a huge fuss? Besides, they come up to a method in which humans are no longer required, just a computer.

Yes! The paper by S. MacGroBen is indeed reason for a HUGE fuss! It substantially enables the program sketched out by Steven Weinberg at a CERN conference on around 6 July 2009. Basically unification based on quantized gravity and the "good old standard model".

The fuss I was talking about, which may have been a useless 30 year diversion, is the fuss that was made based on the assumption that Einstein gravity is inherently non-renormalizable and some radical break with GR is required.

 

[tom.stoer]

(a) all I can calulate are correlation functions
(b) I have no procedure for measuring these correlation functions within the universe
(c) all I can do is calculate S-matrix using LSZ type formulae
Therefore, I have no realistic theory of observation.

rearding a) where did I say that?
rearding b) where did I say that? how does a simple theory like Newtonian mechanics tell you how to measure things?
rearding c) where did I say that?

 

[atyy]

The fuss I was talking about, which may have been a useless 30 year diversion, is the fuss that was made based on the assumption that Einstein gravity is inherently non-renormalizable and some radical break with GR is required.

Exactly, LQG will be a failure.

String will still be interesting, because theories fail even if they are renormalizable.

 

[marcus]

Exactly, LQG will be a failure.
...

You sound quite sure of that.

 

[atyy]

You sound quite sure of that.

Let me say more carefully - the poor conceptual foundations of LQG will be shown up.

LQG will survive as GFT, but all the heuristics in Rovelli's Quantum Gravity book will be discarded.

 

[MTd2]

Exactly, LQG will be a failure.

String will still be interesting, because theories fail even if they are renormalizable.

So, both of them will fail?

 

[atyy]

So, both of them will fail?

For example, there could be a UV fixed point of pure gravity, but we are off the critical surface. I believe that even in this case, although AS will not describe reality perfectly, the fixed point will have some influence on nearby trajectories and thus be physically visible.

At the same time, it will imply that gravity is emergent. I would be interested to know if the existence of AS is compatible (or provably not) with string theory in this fashion.

 

[MTd2]

I don`t see how that relates to LQG.

 

[Careful]

rearding a) where did I say that?
rearding b) where did I say that? how does a simple theory like Newtonian mechanics tell you how to measure things?
rearding c) where did I say that?

So then, enlighten us with the brilliant scheme you have in mind If I may assume that by asking these questions you are suggesting you have something else in mind, then go ahead.

You make moreover the mistake many people make, you see the lack of a measurement theory in Newtonian mechanics as a reason for not defining one in QM. Well, you are plain wrong; the point is that Newtonian mechanics is a selfconsistent theory which allows for the construction of a theory of measurement within it's own limitations. Quantum mechanics does not enjoy that nice property, that was the gist of the original Bohr - Einstein debate from the beginning.

Careful

 

[Careful]

The fuss I was talking about, which may have been a useless 30 year diversion, is the fuss that was made based on the assumption that Einstein gravity is inherently non-renormalizable and some radical break with GR is required.

Look, let me put it simple: the strategy of performing a ressumation of the normal perturbation expansion and thereby getting a renormalized theory was known to many people in the 1970 ties. The point is -as I said before- that you are completely losing control over the physics; you are just making a mathematical excercise. The physical motivation behind the ordinary expansion is much deeper than you may imagine. And no, people do not only think a ''radical'' break with GR is required, a ''radical'' break with QM might be necessary as well.

Careful

 

[atyy]

I don`t see how that relates to LQG.

AS postulates gravity is fundamental.

So does LQG, in its original form.

AS is much more to the point, than LQG's conceptual basis, which as far as I can tell, is that "relativists think deeply".

 

[Careful]

which as far as I can tell, is that "relativists think deeply".

Well, some relativists do :tongue:

 

[marcus]

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

Sauer MacGroben sounds like a real Scotchman.

Maybe we should remember the names of the authors (of this thread's topic paper) in reverse alphabet order:

Saueressig Machado Groh Benedetti

 

[MTd2]

AS postulates gravity is fundamental.

So does LQG, in its original form.

AS is just a state the results from a non perturbative method. You can see it applied to different theories in the paper. This method is, given its name, insensitive to perturbative quantization, so, Feymann graphs doesn`t change the AS point. At least, qualitatively.

Now, LQG is a non perturbative quantization, so it should be expected that it actually changes the nature of the AS point. Maybe quantize it.

 

[Careful]

AS is just a state the results from a non perturbative method. You can see it applied to different theories in the paper. This method is, given its name, insensitive to perturbative quantization, so, Feymann graphs doesn`t change the AS point. At least, qualitatively.

Would you care to define what nonperturbative quantization means in the path integral language please ? It is easy to use buzzwords, but it is harder to say what you mean right. :tongue2: I understand what people talk about when they say that they perform resummations of the perturbation series, I also understand what they mean when they discretize, likewise so following the ordinary Dirac quantization. But I don't know what they mean with nonperturbative method because it might very well be that all previous recipes are inequivalent.

Now, LQG is a non perturbative quantization, so it should be expected that it actually changes the nature of the AS point. Maybe quantize it.

LQG is not a nonperturbative quantization, LQG is a new type of ''quantization''; actually we don't know what it is. That it is not a quantization was proven by Robert Helling six years ago.

 

[tom.stoer]

LQG is not a nonperturbative quantization, LQG is a new type of ''quantization''; actually we don't know what it is. That it is not a quantization was proven by Robert Helling six years ago.

It is both new and intrinsically non-perturbative (no G, G², ...); there is the famous LOST theorem which proves its uniqueness; what do you mean by "it is not a quantization" and where's the paper? has it been published?

 

[Careful]

It is both new and intrinsically non-perturbative (no G, G², ...); there is the famous LOST theorem which proves its uniqueness; what do you mean by "it is not a quantization" and where's the paper? has it been published?

That's too funny, all this LOST theorem did as far as I recall, was to prove uniqueness of cyclic representation soving SPATIAL diffeomeomorphism constraints. The devil is in the details of course and you need to show, for starters, that a proper Hamiltonian can reside there. The paper is the famous one of Helling where he shows that LQG quantization gives inequivalent results to standard quantization for something as simple as the harmonic oscillator. Now, I assume you know the Stone Von-Neumann theorem concerning representations of the Weyl algebra for finite dimensional quantum systems? Therefore any ligitimate quantization should give the same results and polymer quantization doesn't, ok ?

 

[Haelfix]

Sigh, I just had a long reply eaten!

Anyway I was just pointing out that this paper does not make the claims that this thread seems to imply.

Technical aside:

1) Background independance here means a weak form found eg in semiclassical gravity or in perturbative string theory. Namely that after you perform a background field split, the metric g is left arbitrary and not fixed. In other words you can carry it through to the end of the calculation, and don't need to make many assumptions about the nature of the geometry a priori. Whereas in previous numerical work, certain boundary conditions and symmetries needed to be there (by hand) in order to make the calculation tractable (eg spherically symmetric spacetimes or perhaps flat space) and you have to start from scratch if you wanted something a little different.

So while this is a technical advantage (indeed it is one of the virtues of the heat kernel expansions pionered by De Witt) it is still merely another algorithm and expansion/truncation method and merely reverifies the fixed point structure found in previous papers using the functional exact renormalization group methods.

So, in the AS program in general, the prescription is you

1) take some fundamental effective lagrangian (in this case gravity, but not necessarily restricted to gravity).
2) Perform some sort of expansion or regularization scheme (point splitting, zeta function, heat kernel etc etc)
3) Simplify the resulting expression (which for instance will contain an infinite amount of couplings or at least operators or objects hiding an infinite amount of couplings) either by truncating the series or by choosing something more subtle (eg 1/N expansions) in order to simplify the computational task.
4) Feed it back into your favorite algorithm (ERGE, or other) that will capture some amount of nonperturbative information.
5) Get a result about the flow equations, and potentially the nontrivial fixed point structure.

The fundamental problem with this whole business, and what basically most of the theorists I have asked state, boils down to universality classes. In other words, the theory you started with, is not necessarily what you end up with. Whenever you do violence to the perturbation expansion in step 3, you have to really worry about whether or not step 4 is probing something *else* (possibly spurious fixed points for instance) outside of what you are interested in.

Really you need some additional piece of independant, analytic results in order to verify the existence of the fixed point structures (for instance in other areas of particle physics the existence and nature of the Wilson-Fisher fp was independantly derived through several different methods).

On the plus side, this paper has the potential to do something rather neat. It turns out that the heat kernel expansions are technically problematic after 1 loop. However there is a difficult but doable generalization and fix, which allows I believe up to 2 loops. That is important here, b/c it would allow in principle the inclusion of the Goroff-Sagnoti term in pure gravity, which is really the first dangerous coupling in gravity.

Inclusion of that term has up to now, resisted analysis for complexity reasons. Hopefully, this paper changes that.