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

[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

 

[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. 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.

 

[Careful]

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.

That's what I said in my first post.

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.

I thought it was just another perturbative algorithm. I didn't look into the paper, but since you talk about heat kernel, I assumed everything they do is euclidean gravity right ?

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.

Right, you have no control over the physics.

Careful

 

[tom.stoer]

The loop guys turn this round and say that if you want to a reasonable NEW result you need a NEW quantization.

Which paper shall I look at?
http://arxiv.org/abs/hep-th/0409182
http://arxiv.org/PS_cache/hep-th/pdf/0610/0610193v1.pdf

Do you know
http://arxiv.org/abs/gr-qc/0610072
which says

"In this paper, a version of polymer quantum mechanics, which is inspired by loop quantum gravity, is considered and shown to be equivalent, in a precise sense, to the standard, experimentally tested, Schrödinger quantum mechanics ...

... and that is unitarily equivalent to the Schrödinger representation of quantum mechanics. As a concrete implementation of our formalism, the simple harmonic oscillator is fully developed.

... Even when it might seem that our results contradict in a sense the results of [7], this is not the case."

Eventually I would like to say that this might be totally irrelevant at all. If it is possible (and the work of Rovelli et al. suggests this) to define a spin network Hilbert space which describes quantum gravity and has the correct semi-classical limit, then the procedure to derive this qm framework is irrelevant. Quantization is an ad hoc method that cannot really be motivated - except for the obvious fact that it works. So if you have a consistent theory of quantum gravity that agrees with GR at low energies then ...

 

[Careful]

The loop guys turn this round and say that if you want to a reasonable NEW result you need a NEW quantization.

Which paper shall I look at?
http://arxiv.org/abs/hep-th/0409182

You can turn around as much as you like, but the harmonic oscillator is well tested as a good approximation to several physical systems. This paper will suffice to get a first impression.

Do you know
http://arxiv.org/abs/gr-qc/0610072
which says

"In this paper, a version of polymer quantum mechanics, which is inspired by loop quantum gravity, is considered and shown to be equivalent, in a precise sense, to the standard, experimentally tested, Schrödinger quantum mechanics ...

... and that is unitarily equivalent to the Schrödinger representation of quantum mechanics. As a concrete implementation of our formalism, the simple harmonic oscillator is fully developed.

... Even when it might seem that our results contradict in a sense the results of [7], this is not the case."

I remember vaguely this paper, as I remember having dismissed it's argumentation. But I don't know the details of my reasons anymore, if you insist, I can take a look at this.

Quantization is an ad hoc method that cannot really be motivated - except for the obvious fact that it works. So if you have a consistent theory of quantum gravity that agrees with GR at low energies then ...

Another point is that LQG doesn't shed any light on this, no ? They are just messing around and trying to extend QM in a way which contradicts standard QM, there is no basis for QT constructed at all.

Careful

 

[tom.stoer]

They are just messing around and trying to extend QM in a way which contradicts standard QM, there is no basis for QT constructed at all.

No. They perhaps mess up the derivation of a QT, but not the QT itself:
- they have a separable, physical Hilbert space
- they have an inner product
- ...
So there's a problem how to DERIVE all this, but this is not a problem at all!

Look at a house and at a drawing of a house. Why do you think that problems in constructing houses does affect existing houses at all? If you are able live in a house it's academic to think about how it came into being.

So I agree that LQG does not claifiy all open issues regarding quantization, but that does not necessarily mean that everything is b...sh.. it's work in progress

 

[Careful]

No. They perhaps mess up the derivation of a QT, but not the QT itself:
- they have a separable, physical Hilbert space
- they have an inner product
- ...
So there's a problem how to DERIVE all this, but this is not a problem at all!

And who says that these are the correct structures for QT? Perhaps you should read the original remarks Von Neumann made towards Hilbert space construction. You should always listen to genius, not people who repeat words of people who give their own interpretations of people who read genius.

Look at a house and at a drawing of a house. Why do you think that problems in constructing houses does affect existing houses at all? If you are able live in a house it's academic to think about how it came into being.

But people who build a house understand why a house should be build that way. The understand Newtonian physics and the underlying laws of nature. This reminds me of a joke of a civil engineer constructing bridges and oeps he forgot to take gravity into account in his design Point is, that you only construct house, once you understand why it will remain stable: people in LQG have not even remotely an idea why this should be the case.

So I agree that LQG does not claifiy all open issues regarding quantization, but that does not necessarily mean that everything is b...sh.. it's work in progress

Sure it is, for many of the reasons mentioned above. I advise you to read the following beautiful paper which might help you to begin to understand the problem of quantum gravity
http://www.vub.ac.be/CLEA/aerts/publications/2004QuoVadisQM.pdf
Now, this is physics, not merely some misguided mathematical excercise.

Have fun with it.

Careful

 

[MTd2]

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).

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

 

[Careful]

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

Let me answer: no, but people do not regard their numerical excercises as a ''breakthrough'' either. It was said on the first page that the TITLE of this thread is the problem, not so much the paper.

Careful

 

[atyy]

Right, you have no control over the physics.

I don't understand why you call that mathematically ok, but no control over the physics. Surely the problem with step 3 is mathematical, since one clearly does not want a truncation.

In fact this is a problem even in condensed matter systems. It's just that there the experiment can be done to check that the lack of mathematical control was luckily ok.

BTW, one doesn't have to look to Helling to see LQG's inconsistency. A recent Rovelli review admits the theory is probably in 2 ways - an infrared divergence, which I agree may not be problematic, and a divergence of the scalar product, which I understand to be a "UV" divergence in spirit, although for technical reasons Rovelli reserves that term for somnething else, so he is able to say that there are no UV divergences.

 

[Careful]

I don't understand why you call that mathematically ok, but no control over the physics. Surely the problem with step 3 is mathematical, since one clearly does not want a truncation.

In principle, it could be that if you take higher and higher truncations, you get a convergent series; so it might be mathematically well defined - but then, as far as I understand, the physics may depend upon the way you take the limit (which is not healthy at all).

In fact this is a problem even in condensed matter systems. It's just that there the experiment can be done to check that the lack of mathematical control was luckily ok.

One cannot know everything

BTW, one doesn't have to look to Helling to see LQG's inconsistency. A recent Rovelli review admits the theory is probably in 2 ways - an infrared divergence, which I agree may not be problematic, and a divergence of the scalar product, which I understand to be a "UV" divergence in spirit, although for technical reasons Rovelli reserves that term for somnething else, so he is able to say that there are no UV divergences.

Haha, why continue reading nonsense when you know it to be so ? I need my time for better things - I had my period that I gave LQG a chance. It is long over.

Careful

 

[unusualname]

A... I advise you to read the following beautiful paper which might help you to begin to understand the problem of quantum gravity
http://www.vub.ac.be/CLEA/aerts/publications/2004QuoVadisQM.pdf
Now, this is physics, not merely some misguided mathematical excercise.

Have fun with it.

Careful

"If our explanation for the quantum structures is the correct one, quantum mechanics is compatible with a deterministic universe at the deepest level."

FAIL

"There is no need to introduce the idea of an ontological probability"

That would be ridiculous.

 

[Careful]

FAIL

No fail The authors say *compatible*, it doesn't imply it would be *natural*. I would certainly agree that it is not natural, but also that it is possible.

That would be ridiculous.

Do you even know what that sentence means ? Oh yes, how was your first visit to the doctor ?

Careful

 

[unusualname]

No fail The authors say *compatible*, it doesn't imply it would be *natural*. I would certainly agree that it is not natural, but also that it is possible.



Do you even know what that sentence means ? Oh yes, how was your first visit to the doctor ?

Careful

I think you should be wary of papers which proudly exclaim how the arguments are based on "long and really hard mathematical proofs", remember your hero Von Neumann fumbled a relatively simple argument disproving hidden variables, and no one even noticed (for several decades)

 

[Careful]

I think you should be wary of papers which proudly exclaim how the arguments are based on "long and really hard mathematical proofs", remember your hero Von Neumann fumbled a relatively simple argument disproving hidden variables, and no one even noticed (for several decades)

Well, Johnny's argument was wrong, likewise so for Bell's argument. But the paper I mentioned has no problem with those things; actually, I didn't say that I agree with everything the authors say, I find it an interesting paper which certainly contains a few very good ideas.

And certainly it shows that new conceptual work is needed to marry these two theories.

What i am wary of are single sheet A4 theories of everything.

Careful

 

[unusualname]

Well, Johnny's argument was wrong, likewise so for Bell's argument. But the paper I mentioned has no problem with those things; actually, I didn't say that I agree with everything the authors say, I find it an interesting paper which certainly contains a few very good ideas.

And certainly it shows that new conceptual work is needed to marry these two theories.

What i am wary of are single sheet A4 theories of everything.

Careful

LOL. It would probably only be a TOE if gravity is statistical, but we'll see

Anyway, sorry for taking the thread off-topic, but you seemed to be building up to something big over the last few weeks, with an impressive command of modern physics, and a very dismissive arrogant tone, I expected something pretty special, as I'm sure did others.

 

[Careful]

Anyway, sorry for taking the thread off-topic, but you seemed to be building up to something big over the last few weeks, with an impressive command of modern physics, and a very dismissive arrogant tone, I expected something pretty special, as I'm sure did others.

The sane thing to do is to first discuss your work with friends (professors, post-docs), then with some specialists in different fields and then you hand it in after review to some editor. Everybody can be wrong including me, and you have to be pretty damn sure that there is a good chance your theory will pass many non-trivial consistency checks before you give it away to the lions. Those things are not done on a forum and there is always some time span between finishing up the writing process and handing it in for peer review. Having the laws is not sufficient, you also need to solve them in some nontrivial cases and show that results pretty much agree with what one would expect, that is the (second part of the) hard work! If you would have say a new quantum theory, you would have to reproduce a whole new calculation method a la Feynman, Schwinger to solve the interacting case.

Another thing is not to mix this up with severe dismissal of known ideas and consider that to be arrogant. Actually I know all these ideas deeply because I have rediscovered them all by myself. Dismissal is crucial in making progress.

The paper I referred to contains -as I said- many useful elements.

Careful

 

[marcus]

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

So it turns out that probably gravity is renormalizable after all. This is in the sense that top people in the field use the term---nonperturbatively renorm'ble.

I'm curious as to why some people seem to find this threatening? Why do some folks get defensive and start making loud denial noises? Does it upset anybody's applecart?

 

[Careful]

So it turns out that probably gravity is renormalizable after all. This is in the sense that top people in the field use the term---nonperturbatively renorm'ble.

I'm curious as to why some people seem to find this threatening? Why do some folks get defensive and start making loud denial noises? Does it upset anybody's applecart?

Arguing against politicians instead of scientists is a lost case, since the former have very different motives. And why would people find it threatening if someone found a genuine solution to quantum gravity which is perpendicular to their approach ? It is not because we are in hard competition that we don't recognize a (partial) solution when it is in front of us you know. Not everyone has the same personality, ambition, ruthless honesty, and so on and that is ok; it is normal in a society. These debates about sociology of science are really non issues in standard scientific institutes; you may find them interesting, but I am afraid you are betting on the wrong horse. The only thing which is dangerous are people who blow up the importance of a paper by a magnitude of 60 e-folds; this is in the first place very unpleasant for the authors and in the second it prohibits having a balanced discussion about the status of their work.

Careful

 

[marcus]

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

One can, I guess, call Steven Weinberg and Roberto Percacci politicians. They clarified and spotlighted the perturbative renorm'ble thing last year. Weinberg in his 6 July CERN talk and Percacci by organizing the AsymSafety conference at Perimeter, which Weinberg announced in July and then later attended.

Science leadership requires some political and diplomatic skill. Weinberg made the point with extreme tact, speaking especially to string people.

It sounds like an ad hominem smear to label someone who points out the nonperturb. renorm'bility of gravity as a "politician". It strikes me as mildly disgusting innuendo rather than rational argument.

The very simple logical point is that IF gravity has a UV fixed point in a finite dim critical surface THEN (as Weinberg already pointed out in his 1976 Erice talks) the theory is predictive to arbitrarily high energy once a finite number of parameters are fixed. This is what perturb. renorm'bility achieves as well, and it is what is meant by nonperturbative renormalizability.

 

[Careful]

One can, I guess, call Steven Weinberg and Roberto Percacci politicians.

No, you can't: I actually listened to the first 30 minutes of the Weinberg tape you mentioned and he was much more modest about this approach than this thread reveals.

They clarified and spotlighted the perturbative renorm'ble thing last year. Weinberg in his 6 July CERN talk and Percacci by organizing the AsymSafety conference at Perimeter, which Weinberg announced in July and then later attended.

It is OK to spotlight your ideas, but when you give a scientific talk, you actually mention the results and achievements. And Weinberg did that in a very correct way. He merely said these results were encouraging, but he immediately mentioned lot's of pitfalls.

Science leadership requires some political and diplomatic skill. Weinberg made the point with extreme tact, speaking especially to string people.

No, science leadership does not require this; for example Newton was a rude autistic person, Emmy Noether was boorish, Lev Landau had typical russian style towards ''stupidity''. There are different reasons why people are polite and or diplomatic: (a) either it is just their nature (b) they feel very uncertain about their own results and certainly take care not to overhype (c) they just want to avoid ''unpleasant confict'' and most of all (d) most of us just want to tell about results and do not really care what other people do or think. But none of these reasons includes ''political or diplomatic'' motivations.

It sounds like an ad hominem smear to label someone who points out the nonperturb. renorm'bility of gravity as a "politician". It strikes me as mildly disgusting innuendo rather than rational argument.

It takes one to know one.

The very simple logical point is that IF gravity has a UV fixed point in a finite dim critical surface THEN (as Weinberg already pointed out in his 1976 Erice talks) the theory is predictive to arbitrarily high energy once a finite number of parameters are fixed. This is what perturb. renorm'bility achieves as well, and it is what is meant by nonperturbative renormalizability.

Yes, but that point of view has several difficulties which were highlighted in the video and during the discussions in this thread. Moreover, there are as many views on what quantum gravity ought to solve as there are quantum gravity researchers. My laundry list is more like Penrose's while Weinberg's is a lot more like Hawking's, hence much more modest.

Careful

 

[marcus]

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

The question remains: suppose that gravity has a UV fixed point and finite dimensional critical surface---in other words is nonperturabively renormalizable---what are the consequences and why does this seem to excite a reaction?

Weinberg starting around minute 52 of his 6 July 2009 CERN talk (ask if you want the video link) put it this way, in words to this effect:
===approx quote===
I wouldn't urge anyone to stop doing string theory, but it might not be needed. String theory might not be how the world is. Instead it might just be gravity and good old quantum field theory.
==endquote==

Then there was his talk to the Strings 2010 conference. I gave the link to the video earlier.

Also, did anyone find anything wrong with the paper of Saueressig, Machado, Groh, Benedetti?
I have been reporting Asymptotic Safety talks and papers since about 2005 (when Reuter gave an invited talk about it at Loops 2005 conference) and this paper is, in a sense, just one in a series of noteworthy AS papers. Another one I would consider a landmark paper was by Percacci Codello Rahmede around 2007-2008.
No point quibbling about relative degrees of importance. The current paper is important. Shall we discuss why?