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

[humanino]

You probably know that I keep interest in all those different approaches. To answer

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

Independently of whether nature is stringy at a fundamental level, string theory methods proved invaluable to perform effective calculations of strongly bound systems. These methods apply broadly, from condensed matter to the very birth of strings, namely hadronic systems.

On top of that, you probably also know how twistor and string methods have uncovered new symmetries, dubbed Yangian, in Yang-Mills theories in general. Witten's 2003 paper was his most cited since it was posted, last time I checked. This approach covers from on one side very practical QCD background to LHC signals which were previously thought to be impossible to calculate to on the other side "gravity as the square of Yang-Mills" which Zee has added as a new chapter to the second edition of his Nutshell.

Progress is made by everybody on every side. I remain firmly convinced that no-one is entitled to dismiss the possibility that all those insights will eventually lead to different ingredients for a final theory of QG.

 

[Careful]

Progress is made by everybody on every side. I remain firmly convinced that no-one is entitled to dismiss the possibility that all those insights will eventually lead to different ingredients for a final theory of QG.

You see, that is not how it works. One will only recognize which idea comes back (either as fundamental principle or emergent property) after one has found the correct physical principles. What you say is in a certain sense trivially true, the probability for none of the current ideas to have some resemblance to a better theory is almost as good as zero, but where you get wrong is by suggesting that by considering each of these separate ideas one is somehow going to clear up the picture. That is very wrong indeed, one needs NEW ideas, this was already know to Feynman in the 80 ties and that's why one needs to be dismissive of ''partial'' ''solutions''.

 

[tom.stoer]

one needs NEW ideas, ... and that's why one needs to be dismissive of ''partial'' ''solutions''.

Yes ... No

New idas are indeed needed, but ongoing research must not be halted. The problem is that partially there are too many speculative ideas; that's not healthy for science. We can never be sure to capture entire new physical principles when we are not able to constrain these new ideas via experiments - which is currently the most pressing problem in fidning a theory of QG or unification! Therefore we need everything from rather conservative approaches like AS (no new physics, everything is rather boring up to the Planck scale) and LQG (a rather modest change in the quantization but no new physical principle), strings (indicating that there are new physical principles, but up to now being able to identify them clearly) and perhaps approaches like twistors, causal sets, NCG etc.

There is nobody out there who can safely say that one of these approaches is definately wrong!

 

[Careful]

Yes ... No

New idas are indeed needed, but ongoing research must not be halted. The problem is that partially there are too many speculative ideas; that's not healthy for science. We can never be sure to capture entire new physical principles when we are not able to constrain these new ideas via experiments - which is currently the most pressing problem in fidning a theory of QG or unification!

No it is not! Logical consistency is the most important guideline for quantum gravity. But yeah, you are simply not willing to make that excercise because then you feel dumb. You don't know then what to believe or to think anymore; it is much more safe to stick to a purely technical language even if it doesn't mean anything.

Therefore we need everything from rather conservative approaches like AS (no new physics, everything is rather boring up to the Planck scale) and LQG (a rather modest change in the quantization but no new physical principle), strings (indicating that there are new physical principles, but up to now being able to identify them clearly) and perhaps approaches like twistors, causal sets, NCG etc.

There is nobody out there who can safely say that one of these approaches is definately wrong!

Sure, we can, just investigate inner consistency. Can these approaches start defining thing like observer, observation in a dynamical way ? Do these ''theories'' allow for realistic measurements inside universe ? Are they based on logic grounds ?

Of course, almost no one is willing to make these excercises (except people in causal set approach and thinkers like Isham and Penrose)... You are all discussing about theories who are already dead in that sense from the beginning and then you hold up your little finger and say to someone like me I can only argue by technical means. I do that and reduce the probability of such program to less than 10 % (in my metric), then you see it becomes hopeless and ask me for no go theorems. Again, this is not science, I have better things to do.

Careful

 

[qsa]

Yes ... No

New idas are indeed needed, but ongoing research must not be halted. The problem is that partially there are too many speculative ideas; that's not healthy for science. We can never be sure to capture entire new physical principles when we are not able to constrain these new ideas via experiments - which is currently the most pressing problem in fidning a theory of QG or unification! Therefore we need everything from rather conservative approaches like AS (no new physics, everything is rather boring up to the Planck scale) and LQG (a rather modest change in the quantization but no new physical principle), strings (indicating that there are new physical principles, but up to now being able to identify them clearly) and perhaps approaches like twistors, causal sets, NCG etc.

There is nobody out there who can safely say that one of these approaches is definately wrong!

All these approaches are correct in one sense or another. Each approach carry some fundamental aspect of a final "fundamental model of reality". Some ingredients are not very well cooked, very few still missing. You need a guy with a clear head-maybe you tom- to tie all the particular fundamental together. It is very hard for paid researchers(who are very smart ,but tied to publish or perish i.e tied to specific issues). cool head. maybe a month or two in the mountains, with a stack of the most fundamental papers.

 

[qsa]

No it is not! Logical consistency is the most important guideline for quantum gravity. But yeah, you are simply not willing to make that excercise because then you feel dumb. You don't know then what to believe or to think anymore; it is much more safe to stick to a purely technical language even if it doesn't mean anything.

Sure, we can, just investigate inner consistency. Can these approaches start defining thing like observer, observation in a dynamical way ? Do these ''theories'' allow for realistic measurements inside universe ? Are they based on logic grounds ?

Of course, almost no one is willing to make these excercises (except people in causal set approach and thinkers like Isham and Penrose)... You are all discussing about theories who are already dead in that sense from the beginning and then you hold up your little finger and say to someone like me I can only argue by technical means. I do that and reduce the probability of such program to less than 10 % (in my metric), then you see it becomes hopeless and ask me for no go theorems. Again, this is not science, I have better things to do.

Careful

I agree that a quantum jump type thinking is also needed. But and I mean BUT, if the approach does not yield anything in a reasonable amount of time I think it should be looked upon as a nice exercise and move to another. I have seen so many researches with these nice wacky ideas(typically smaller universities) which they have worked on for year to no avail.just like your friends. But I guess there could always be an exception however unlikely.

 

[Careful]

.I have seen so many researches with these nice wacky ideas(typically smaller universities) which they have worked on for year to no avail.just like your friends. But I guess there could always be an exception however unlikely.

One you do not know my friends, many of them come from big universities. Second, you should not mean this in a pejorative sense since many breakthroughs in science did not come from a big american/european university. Many of them come from more modest places which has it's advantages and disadvantages. Third, you pretend like you can just make quantum gravity without such considerations (and believe me, the jump-process is just a tiny thing), well you cannot. So all you said is that people at big universities typically work on something which cannot work since they do not want to give the appearance that they work on something in which they might fail personally. Better to fail collectively, then nobody will notice; it is an expensive scam to the taxpayer though.

In my opinion, it is better to work on something which has an a priori chance of larger than 20% to work out, than on something which is known to be dead by all reasonable criteria.

 

[marcus]

This is an excellent statement, Humanino!

...Independently of whether nature is stringy at a fundamental level, string theory methods proved invaluable to perform effective calculations of strongly bound systems. These methods apply broadly, from condensed matter to the very birth of strings, namely hadronic systems.

Quite true. Useful as mathematics. Even returning to historical origins: studying hadrons.

This approach covers from on one side very practical QCD background to LHC signals which were previously thought to be impossible to calculate to on the other side "gravity as the square of Yang-Mills" which Zee has added as a new chapter to the second edition of his Nutshell.

Interesting. We should have a thread about "gravity as the square of Yang-Mills" if we haven't had one already. I can sign onto the next statement you make with some slight [additions]:

Progress is [or can be] made by everybody on every side. I remain firmly convinced that no-one is entitled to dismiss the possibility that [any or] all those insights will eventually lead to different ingredients for a final theory of QG.

I heartily agree, including Causal Dynamical Triangulations, Asymptotic Safe gravity, Spectral Geometry (Connes-NCG), Spinfoams and Group Field Theory (EPRL-GFT) and Loop Quantum Cosmology.

No one is entitled to dismiss the possibility that any of these will eventually be seen to have contributed to understanding the smallscale/highenergy geometry of the universe.

Indeed although I respect string theory as a body of mathematical discoveries/methods I learned back in 2003 to be critical of the way the program is managed and suspicious of string apologists precisely because of their vehement (often ill-informed) dismissal of such alternatives.

One can like the math, but not like the statements and behavior of individuals.

This includes the habit of defending (or trying to defend) String by badmouthing Loop. For example:

Loop is just as untestable.
Loop will encounter an "even worse" landscape dilemma.
Loop necessarily breaks Lorentz (implied earlier in this very thread!)
Loop must be wrong for these and these ten reasons.
(The ha-ha contempt defense) Loop researchers are stupid because they don't realize etc.

This kind of talk is symptomatic of insecurity. And why Loop in particular? Perhaps Loop serves here as symbol of a rising tide of alternatives. Or perhaps it actually is especially threatening--I don't know for sure. In any case badmouthing rivals is a poor way to win respect for string.

 

[Careful]

I agree that a quantum jump type thinking is also needed. But and I mean BUT, if the approach does not yield anything in a reasonable amount of time I think it should be looked upon as a nice exercise and move to another. I have seen so many researches with these nice wacky ideas(typically smaller universities) which they have worked on for year to no avail.just like your friends. But I guess there could always be an exception however unlikely.

Just for your information, from all nobelprize winners from 1901 - 1911, only one came from a big university (and no american is in the list of prizewinners); it is lord Rayleigh from Cambridge university. All the rest comes from less reknown places. So, I think your statistics is very wrong.

Careful

 

[Careful]

This includes the habit of defending (or trying to defend) String by badmouthing Loop. For example:

Loop is just as untestable.

It is !

Loop will encounter an "even worse" landscape dilemma.

I have never heard that, but loop certainly will face a landscape dilemma, every approach does.

Loop necessarily breaks Lorentz (implied earlier in this very thread!)

The point is that nobody knows what loop is. Loop is double faced, you have smolin with his ideas about kappa-Minkowki which does violate Lorentz invariance, then you have Rovelli LQG in which Lorentz invariance might be broken at the quantum level (not at the classical one) and then you have Alexandrov construction which is manifestly Lorentz covariant. So you know, it is easy to claim A and NOT A and argue that nobody can say something about A.

Loop must be wrong for these and these ten reasons.

But it is and is proven to be so several times.

But what is symptomatic for loopies is that they offer no reasons PRO loop; they only have a magical word ''background independence''.

 

[marcus]

I like the four sector characterization of the research scene, from "convervative approaches like AS" to "perhaps approaches like twistors, causal sets, NCG etc". I edited the quote to bring out the four-part list aspect:

...New idas are indeed needed, but ongoing research must not be halted. The problem is that partially there are too many speculative ideas; that's not healthy for science. We can never be sure to capture entire new physical principles when we are not able to constrain these new ideas via experiments - which is currently the most pressing problem in finding a theory of QG or unification! Therefore we need everything

from rather conservative approaches like AS (no new physics, everything is rather boring up to the Planck scale)

and LQG (a rather modest change in the quantization but no new physical principle),

strings (indicating that there are new physical principles, but up to now being able to identify them clearly)

[to] perhaps approaches like twistors, causal sets, NCG etc.

There is nobody out there who can safely say that one of these approaches is definately wrong!

All these approaches are correct in one sense or another. Each approach carry some fundamental aspect of a final "fundamental model of reality". Some ingredients are not very well cooked, very few still missing. You need a guy with a clear head-maybe you tom- to tie all the particular fundamental together. It is very hard for paid researchers(who are very smart, but tied to publish or perish i.e tied to specific issues). cool head. maybe a month or two in the mountains, with a stack of the most fundamental papers.

I also like Qsa's response although I don't completely agree. It doesn't have to be amateurs. Paid researchers (like Steve Carlip at Davis) can constructively step back, take a fresh look at the whole picture, and form a new synthesis. It won't be the "final" synthesis necessarily but may contain useful fresh insight. But that's a quibble---the professional/amateur issue doesn't seem so important as long as there is active variety within institutions. Europe may be doing a better job than the USA at present, in that respect.

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

Tom, your point about TESTING and the need for constraining the new theories (lest they become hopelessly lost in speculation):

1. AS. Right now it can probably be constrained by CALCULATION to map out the critical surface. I think calculation can be a game-changer in this line of research. And eventually precise measurement of parameters---there seem to be 3---to check that gravity as found in nature actually lies on the critical surface. Weinberg raised this issue in his AS talk to Strings 2010. He diplomatically insisted he was not there to "sell" AS but quietly pointed out a way it can be tested, mentioned among the "problems" with the theory. His mildness delivers the message while disarming resistance.

2. LQG. It consistently predicts a bounce. And several papers recently indicate that it makes adequate inflation natural/generic---removing much of the need for fine tuning. This has led a bunch of people to start working on ways to test LQG, by what it says about the early universe.

3. Can't say about string.

4. Among the "perhaps" approaches, NCG makes a lot of LHC testable predictions
https://www.physicsforums.com/showthread.php?p=3042880#post3042880

The LQG bid to become less speculative and more empirical is based on the fact that it has a model of the early universe's geometry. And there is a flood of data coming in on that. If you model early universe geometry you get to enjoy that flood of data. And you also risk being ruled out by it. In any case some constraint is in the works there.

 

[tom.stoer]

marcus,

of course I should think about minor corrections regarding my statements and regarding the entire list (there is a typo, regarding strings it should read "but up to now NOT being able to identify them clearly"). Of course discussion is needed.

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!

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.

There was I time when I was thinking that strings are dead b/c they are not testable. 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; then - with Heisenberg et al. - there was a breakthrough; a few years later Dirac discoverd his equation -and run into new inconsistencies; another few years later QED ...)

 

[atyy]

I'm waiting to see if Atyy likes this one:

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

"almost persuasively" makes it too long. A headline has to be brief. It almost necessarily oversiumplifies but then you can look at the article itself to get the nuances and qualifications etc. etc.

No I don't like it either.

Both parts are misleading.

The first part of the suggested thread title is misleading because this article does nothing to make AS more persuasive than before. It is a computer algorithm. Yes, I like the paper, and I like AS, and I find all the previous hints intriguing. The thread title is misleading because it gives too much credit to the present work, and does not give sufficient credit to previous work which suggests AS is worth investigating.

The second part of the suggested thread title is also misleading because it makes it seem that people were unaware that AS is a well-motivated possibility (at least from the Wilsonian framework, which is shared between AS, strings, and Rivsseaueque GFT). In fact, it is stated as the alternative hypothesis in chapter 1 of Polchinski's standard textbook on strings. AS is just difficult to investigate because although Wilson indicates that non-perturbative fixed points must be ruled out before declaring a theory unrenormalizable, it is mathematically very difficult to find non-Gaussian fixed points (and perhaps even more difficult to prove their non-existence). Furthermore, even if AS is true, by virtue of strings as a consistent theory of quantum gravity, we will have to find out how the two fit together. For example, could we be off the critical surface, so that at lowish high energies, we will see the fixed point, but at even higher energies we will see strings? This is close to what Percacci says, except that he doesn't want to bet on the proper UV completion if we are off the critical surface (and neither do I, except that strings is the only example I have at the moment).

If there's any group of QG investigators who have not taken AS seriously enough, it is Rovellian LQG (Smolin clearly investigated it early, and got stuck because of the same difficulties that remain).

 

[MTd2]

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.

 

[humanino]

You see, that is not how it works. [...] suggesting that by considering each of these separate ideas one is somehow going to clear up the picture.

This is not what I suggested. I suggest to be "careful" and respectful of other's work. If the maths is right, it might somehow prove useful in the future. You know Polyakov's quote from "gauge fields and strings"

The garbage of the past often becomes the treasure of the present (and vice-versa)

I think I have argued enough with you whether the glass is half-full or half-empty. I believe we do not really disagree, we just approach the role of this forum quite differently. Bashing other's people work caused Motl to loose his academic position. I do not care for such behavior.

 

[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