Weinberg cites Reuter, Saueressig, also Percacci in Oriti's Quantum Gravity book

[marcus]

Interesting that Steven Weinberg should cite Asymptotic Safety work by Martin Reuter and Frank Saueressig. And another UV-safety article by Roberto Percacci, that appears in Oriti's new book Approaches to Quantum Gravity: Towards a New Understanding of Space, Time, and Matter.

Here's a bit from page 14 of Weinberg's recent essay http://arxiv.org/abs/0903.0568 :
"...But it need not lose its predictive power at high energies, if the renormalized coupling constants g_n (E) at a renormalization scale E approach a fixed point g_n∗ as E → ∞. [30]
This is known as “asymptotic safety.” For this to be possible, it is necessary that β_n (g_∗) = 0, where β_n(g (E)) ≡ E dg_n(E)/dE.

It is also necessary that the physical coupling constants g_n(E) at any finite energy lie on a trajectory in coupling constant space that is attracted rather than repelled by this fixed point. There are reasons to expect that, even with an infinite number of coupling parameters, the surfaces spanned by such trajectories have finite dimensionality, so such a theory would involve just a finite number of free parameters, just as for ordinary renormalizable theories.

The trouble, of course, is that there is no reason to expect the g_n∗ to be small, so that ordinary perturbation theory can’t be relied on for calculations in asymptotically safe theories. Other techniques such as dimensional continuation, 1/N expansions, and lattice quantization have provided increasing evidence that gravitation may be part of an asymptotically safe theory. [31]
So it is just possible that we may be closer to the final underlying theory than is usually thought."

Here are the references [31] which Weinberg cites:

[31]
M. Reuter and F. Saueressig, 0708.1317; R. Percacci, in Approaches to Quantum Gravity: Towards a New Understanding of Space, Time, and Matter, ed. D. Oriti (Cambridge Univ. Press) [0709.3851]; D. F. Litim, 0810.3675; and earlier references cited therein.

Prepublication copies of Oriti's book are already in stock and on sale from several dealers
http://www.amazon.com/gp/product/0521860458/?tag=pfamazon01-20
https://www.amazon.com/gp/product/0521860458/?tag=pfamazon01-20
although the main amazon does not have it in stock yet.

 

[atyy]

Asymptotic safety goes back to Weinberg himself, among others.

 

[marcus]

Asymptotic safety goes back to Weinberg himself, among others.

Among others? I never heard of anyone but Weinberg being the inventor of the approach.
Back in 2007 I started a thread about Weinberg's initial attempt (in the late 1970s, 1979 if I remember right) to get asympt. safety to work and what if it had succeeded? Here's the thread
https://www.physicsforums.com/showthread.php?t=180119

At any rate Weinberg cites himself in this essay as the initiator and gives the usual 1979 publication reference for it.

I think it's great that thirty years later, essentially 30 years since he has worked on it, he presents it as a real possibility and hands out some credit to Reuter, Saueressig, Percacci and Litim. Reuter and Percacci are people whose work we have discussed a lot here at Beyond forum. Reuter has given plenary talks at several of the Loops conferences and workshops.

Actually Weinberg presents UV-safety as an alternative to having to get something like string theory to work which might never happen or take a long time. He has a paragraph on the "something like string" prospect and then he says but there's an alternative, A.S., and we might be closer than we think.
It's an interesting perspective piece, and quite different from the Weinberg overview I heard him give back in 2005.

 

[atyy]

Among others? I never heard of anyone but Weinberg being the inventor of the approach.
A year or two back I started a thread about Weinberg's initial attempt (in the late 1970s if I remember right) to get asympt. safety to work and what if it had succeeded?

At any rate Weinberg cites himself in this essay as the initiator and gives the usual publication reference for it.

Well, I was just being cautious, in case there were others :) I was thinking roughly that asymptotic safety is one of the logical possibilities that comes from viewing the standard model as an effective theory, which goes back to Kenneth Wilson (and there there really has to be among others - Kadanoff, Gell-Mann and Low etc, though it was Wilson that really brought it all together).

 

[atyy]

Marcus, I sense you are quite enthusiastic about AS? What puzzles me is that isn't the philosophy of AS quite opposed to that of LQG? In fact isn't AS philosophy is closer to string philosophy? They differ as to what the true degrees of freedom are, but both take an effective field theory viewpoint. LQG really stresses "background independence". But I wonder if there could be accidental convergence between AS and LQG given Modesto's result.

 

[marcus]

...asymptotic safety is one of the logical possibilities ...

Yes the basic idea is beautifully simple and straightforward. Weinberg gives an excellent concise description, which actually coincides point for point with Percacci's chapter in Oriti's book. The hard part, as he points out, is making sure that the fixed point exists (in what it an infinite dimensional space).
And you have to identify a finite dimensional "critical hypersurface" of points that are attracted by the fixed point.

Considerable progress has been made on just that problem recently. A paper by Saueressig et al just last week.

Once you have that, then you have the moral equivalent of (nonperturbative) renormalizability, because once you specify a finite number of parameters (putting you on the hypersurface) your theory is fully predictive to arbitrarily high energy.
Weinberg makes the point nicely---as does Percacci.

We've had a lengthy and enjoyable discussion of that nonperturbatively renormalizable concept here at PF in fact.

 

[atyy]

moral equivalent

I like this term. I've been seeing it a lot recently (last 5 years or so), or has it always been around?

 

[atyy]

I guess one of the questions with AS being a logical possibility within the effective theory viewpoint is - if AS can be proven not to work, would that imply anything for LQG? Within the effective theory view, if AS can be proven unworkable, then the same logic would say that new degrees of freedom must enter. Is there a loophole in there which would allow AS to fail but imply nothing about LQG?

 

[marcus]

G

... or has it always been around?

William James 1906. You'll get me distracted (I love language and expressions like that.)

...Marcus, I sense you are quite enthusiastic about AS?...

People can easily get the impression of enthusiasm. I'm an intent observer. I think quantum gravity research is progressing on several fronts. I'm not a devoted fan of anyone approach. I think several different ways of investigating the microstructure underlying geometry and matter will reveal various things and may converge.

Loops 2005 (Potsdam) brought in Renate Loll and Martin Reuter as invited plenary speakers and they emphasized their corroboration of each other.
The non-string QG community is all one community.
They all reinforce each other a lot.
Then Loops 2007 (Morelia) brought in Loll's co-author Jan Ambjorn, and of course Martin Reuter, for invited plenary talks. And again they each emphasized the surprising agreement of their different approaches.
At Loops 2008 (Nottingham) both Loll and Reuter were again there.
Meanwhile Loll, Ambjorn, Reuter, and other CDT and A.S. people have been appearing together along with LQG people at various schools and workshops in Poland, UK, Holland.

I don't know why they don't mix more with String folks, probably because all these non-string approaches are working on 4D and they have no reason to fantasize about 11D or whatever. And String folks don't invite them to their conferences as a rule. So even though there is lots of conceptual overlap in an abstract sense there is little real compatibility.

Reuter has made a big point about A.S. being background independent in the sense that LQG people use the term. Does not depend on a fixed background metric. He spent a lot of his Loops 2008 talk on that (which to me was not the most interesting part). Obviously he wants A.S. to belong to the B.I. QG community. Also Loll considers her CDT approach background independent even though there is a causal ordering, a slicing.

I don't care so much about the minor differences. 1915 General Relativity is clearly B.I. in a simple way. It requres no background metric. The nonstring QG people are all trying to follow GR in that. They are making an effort to build their theories on no preliminary fixed geometry and they pretty much succeed. I'm not a doctrinaire stickler. As I see it, nature has no fixed geometry so one ought to try and avoid elaborate set-ups as much as possible. And string bores me because it is way over the top in the elaborate background direction.

So you can say I'm inconsistent but I am interested in the whole nonstring QG research community and I try to watch whatever is developing rapidly and getting new results.

 

[marcus]

I guess one of the questions with AS being a logical possibility within the effective theory viewpoint is - if AS can be proven not to work, would that imply anything for LQG? Within the effective theory view, if AS can be proven unworkable, then the same logic would say that new degrees of freedom must enter. Is there a loophole in there which would allow AS to fail but imply nothing about LQG?

You may be a lot better than I am at this kind of close reasoning. I don't normally pick winners anyway.
What I would say is it looks fairly likely to me that both LQG and AS are working out.
And if both work, then both will shed some light on the microscopic structure of spacetime.

And that will help inspire and shape the next theory or theories.
Presumably we want a new understanding of space time and matter. We want to know the common fundamentals underlying all three and how matter can effect geometry. We want matter to turn out to be an aspect of geometry, like kinks in geometry, so it is all one thing and it becomes obvious the means by which matter shapes geometry and geometry guides matter.

LQG is a very good start because the spinnetwork is a quantum state of geometry which is definable abstractly without a manifold, and matter fields can live on a spinnetwork, without needing any manifold to be defined on. So the fields can live on each other instead of on a continuum and that's probably like nature--so it's a good start.

Maybe LQG is best, so far. Could be. But best is not so important. All these 4D approaches are valuable and they can all help show the way. Reuter A.S., Loll CDT, Rovelli et al LQG. They don't conflict. They are all following GR (which is background independent) from the very outset and they are all 4D and trying to show us something about the the fundamental microscopic degrees of freedom of natural geometry and matter.
==============

EDIT I'm enjoying our coversation but it's 12:30 AM here so I'll off to bed and resume in the morning

 

[atyy]

And string bores me because it is way over the top in the elaborate background direction.

But what about AdS/CFT, where the CFT is 4 dimensional? I know they haven't got that for de Sitter space yet, but that seems to be really interesting signpost.

So you can say I'm inconsistent

Ah, that's ok. As you know I'm a fan of Wen's crackpot physics, just on the basis of personal aesthetics.

 

[marcus]

I haven't got ready answers to what you just said so I don't see how to continue the conversation! But I liked the discussion so I'll think of something more to say. Or maybe you will. I didn't remember you were interested in XG Wen's ideas.

 

[atyy]

I just read the Weinberg essay you linked to in the OP. It's beautiful in the physics and personal narrative.

Yes, I'm a Wen fan. His approach is descended from Sakharov, Volovik, Visser etc which I'm attracted to because the curvature of spacetime cannot be seen without matter. But science apart, what I really love are the crackpot things in his papers like "Last night a child asked me..." or we live in "noodle soup".

Anyway, from this condensed matter view, what's attractive about strings is that in AdS/CFT it really provides an example in which space and matter "emerge" together. Another reason string theory makes sense to me is that it develops from the renormalization group and effective theory point of view, which is very much a condensed matter thing. This is also why Asymptotic Safety makes sense to me.

Philosophically, this is quite different from the emphasis on the background independence of mainstream LQG. I'm particularly unfond of Rovelli's relativists over particle physicists motivation. On the other hand, I love the crackpot LQG ideas of Smolin, Markopolou, Sundance-Bilson, Yidun Wan, because of their closeness to the condensed matter viewpoint. So this is obviously very inconsistent of me, since Smolin and Markoupoulou were part of mainstream LQG at one time!

Actually, one of the interesting things about Smolin is that in the 1980 Weinberg-Witten paper which eliminates a whole class of condensed matter models of gravity, there is a footnote listing then extant models not eliminated by the theorem - and one of Smolin's papers is among them.

Anyway, back to the topic at hand. I have no clue whether the failure or triumph of AS would imply anything for LQG, it'll be interesting to see how that turns out.

 

[marcus]

Atyy,

Peter Woit has called our attention to Percacci's A.S.Website
with this Asymptotic Safety FAQ:
http://www.percacci.it/roberto/physics/as/faq.html

Some of the writing at the website looks like it grew out of the review article on A.S. that Percacci contributed as a chapter in Oriti's book.
The book also as Q and A at the end of each section.

Percacci has a bibliography for A.S. Here's the main link
http://www.percacci.it/roberto/physics/as/

The UVsafety program has been working out. They find more and more solid evidence that the UV-fixed point exists and attracts a finite dimensional subspace. Maybe only 3 or 4 parameters, the fewer the better. So suppose it works out that way and it's reasonable to accept that gravity is (in this special sense nonperturbatively) renormalizable. Fix 2 or 3 or 4 values and you are good to go. Predictive theory. You are asking if this would have any consequences for LQG. Well the CDT people and the LQG people have been making common cause with Reuter and Percacci. Postdocs cross back and forth. CDT folks especially seem to like every sign of A.S. progress. What can I say? The researchers act like they think it would be good if the A.S.program succeeds.

There is a simpleminded idea that everybody should hate their rivals and it's zero sum. If A.S. gains then there is less glory for CDT or LQG. That doesn't make sense to me. I mistrust the abstract arguments to that effect.

I should be able to do better for you, give you a more articulate answer. Let me try another way to look at it. You know those famous quotes from Einstein in 1916 where he says points in spacetime have no physical reality, and another time he says no objective reality. Ultimately in GR there is no manifold, no math object representing the continuum.

There were those famous 3 years from 1912 to 1915 when Einstein struggled with this and finally accepted it and went ahead. He resisted the message of General Covariance for 3 years even though he knew he was in a race with David Hilbert (top mathematician of the day). The message is there is no continuum. You use it as temporary scaffold in setting up and then in the end you factor it out. A geometry is an abstraction that does not live on a particular continuum and it is the geometry that is real, in nature.

I can get some links if you don't know the quotes.

Perhaps that is the deepest lesson about nature to take away from GR. No theory can be fundamental if it treats differential manifolds as real.

Relativists (with GR background) who venture into QG tend to take the legacy of GR seriously. They take GR as a starting point.

Other folks approach it from Quantum Field Theory (which is NOT general relativistic, only special, doesn't have the key feature of GR like general covariance.) Many of them, I suspect, have the attitude "GR is not renormalizable so it can't be fundamental so we don't have to take it seriously." The idea is that there is something quite different not modeled after GR, underlying, of which GR is just the largescale limit.

EDIT: Oh no! You just said in your post you don't like the-Relativist versus Particle Theorist split!
You don't credit it or want to hear about it and now I'm referring to it!
Well nevertheless I do think the main issue here turns on questions like is GR really renormalizable after all and how seriously should one take what GR tells us about nature?

LQG and A.S. are on the same side of that main divide. That's why my intuitive hunch is that even though they are nominally rivals, if Reuter Percacci et al succeed in persuading everybody that gravity does have a UV fixed point and is (in the special sense Weinberg and Percacci use) renormalizable, though not using a naive perturbation series, then this will be good for LQG.

Both CDT and LQG give ways to visualize microscopic structure and calculate/simulate in ways that A.S. is not. Important gains in anyone of those three will, I think, stimulate research activity across the board.

I haven't given this enough thought. Maybe you should leave me room to change my mind. If you have counterarguments or questions that might probe this issue I would like to hear them. It woud actually help.

 

[atyy]

I would actually guess that Weinberg is on the "non-geometric" side of the relativists versus particle physicist divide. His GR text really downplays GR as geometry,

Yes, I know the famous Einstein remarks about GR taking away the last vestiges of reality from spacetime. But I think another lesson of GR is that spacetime defines matter and matter defines spacetime. From there one might expect that both should emerge from a deeper principle, hence my attraction to condensed matter and string approaches. Another analogy might be to consider thermodynamics, which surely is a deep theory. It's lesson is not that the quantities it deals with such as pressure and temperature are fundamental, but rather they are emergent. But the lesson is indirect, since thermodynamics is internally completely consistent. So yes, I agree that GR is diffeomorphism invariant, but I'm not sure if that is the deep lesson to draw from it. I don't object to a theory motivated by diffeomorphism invariance, but I think it is only one of several aesthetic choices about the deep lesson of GR. Maybe all the lesson will survive, or maybe not. From Newton's original theory of forces, only the Lagrangian and Hamiltonian reformulations seem to work in quantum mechanics.

I guess when I'm more sober, rather than going on gut instinct as to which theories are most wonderfully crackpotty, what I would really like theory to do is to map out and classify the range of internally coherent theories consistent with our present data. From this point of view, a theory that turns out to be experimentally wrong is just as valuable. For example, I think Nordstrom's consistent relativistic theory of gravitation which preceded GR is a great achievement, and I find Whitehead's alternative theory of gravity which contains the Schwarzschild solution fascinating too. I think science is much more fun if we have to do experiments to figure things out. So I think it'd be most fun if AS/CDT, LQG, and string theory or what not all worked out and gave different predictions.

 

[marcus]

I would actually guess that Weinberg is on the "non-geometric" side of the relativists versus particle physicist divide. His GR text really downplays GR as geometry,

I know. A great thing about Weinberg is he changes.
He somehow manages to both respond to and lead changes in emphasis.
He used to be promoting the idea that gravity might not be geometry--e.g. in his text as you say.

But now his shift reflects a resurgence/reconfirmation of that idea. A.S. has as its basis the gravity=geometry idea, extending GR itself to higher energy and smaller scale.

Yes, I know the famous Einstein remarks about GR taking away the last vestiges of reality from spacetime. But I think another lesson of GR is that spacetime defines matter and matter defines spacetime.

These are not contradictory ideas. What your paraphrase of GR should really say is
geometry and matter are in that reciprocal relation.
GR says geometry exists but the manifold, the spacetime continuum does not. It is just a temporary mathematical device used in construction.

By geometry, I mean the gravitational field. Einstein's message was believe in the field. It's real. Material events are located in the field, not on some differential manifold.

I think you have confused the continuum with the geometry and this has led you astray.
Geometry in GR is abstracted from the continuum used to initially define the metric and the continuum is thrown away. That was his point. But geometry is still there and in the reciprocal relation with matter that you indicate.

The big question is "how should we represent the quantum state of geometry?"
Rovelli's idea to use a spin network goes right to this question. Matter fields can be added to the spin network and what it basically is is the quantum state of geometry.

Loll's idea is to use a simplicial complex to represent a geometry. Reuter is trying hold on to the older way, representing the geometry by a metric (an equivalence class of metrics really).

So yes, I agree that GR is diffeomorphism invariant, but I'm not sure if that is the deep lesson to draw from it. I don't object to a theory motivated by diffeomorphism invariance, but I think it is only one of several aesthetic choices about the deep lesson of GR. Maybe all the lesson will survive, or maybe not.

I agree! The approach that gives primary respect for the lessons of GR (background independence, diffeo invariance, no assumption of a physical spacetime, only the field) this approach can be wrong.
Also on the other hand the approach that abandons the lessons taught by GR can be wrong.
That makes it extra interesting--we humans are trying both paths and eventually we will see.
I consider it possible that diffeo invariance can be merely an emergent property. That it is not fundamental that we have at micro level. Only an approximate symmetry emerging at large scale.
Gerard 't Hooft says this is possible in his chapter at the beginning of Oriti's book Approaches to Quantum Gravity. 't Hooft's essay is called "The fundamental nature of spacetime." I didn't get a lot out of it, but he did discuss that idea.

I think science is much more fun if we have to do experiments to figure things out. So I think it'd be most fun if AS/CDT, LQG, and string theory or what not all worked out and gave different predictions.

I agree and I like this statement. I expect at least some of the going approaches will lead to testable predictions and that empirical observation will begin to play a role while we are still around to watch and kibbitz.

 

[atyy]

I expect at least some of the going approaches will lead to testable predictions and that empirical observation will begin to play a role while we are still around to watch and kibbitz.

Now that's an experimentally falsifiable prediction about quantum gravity.