Steven Weinberg offers a way to explain inflation

[Haelfix]

I don't know what he has in mind exactly there, but somehow the field theory has to lose a dimension (not 2 but 1) for the scaling to match. How that is realized, is something that people will need to explain. I'm not saying its impossible, but something peculiar needs to take place. (I am aware of the talk about losing dimensionality, but that's more at the level of the space of coupling constants)

He's very correct that all bets are off in DeSitter space. No one knows or even has an expectation of what the high energy behaviour is like there. There is no SMatrix!

 

[MTd2]

No one knows for sure how many low energy solutions there are in 10^500. Could be infinite , could be finite but very big, there are many ways to count, each one with different plausible consistency conditions. Heh, but isn`t this offtopic?

 

[atyy]

No one knows for sure how many low energy solutions there are in 10^500. Could be infinite , could be finite but very big, there are many ways to count, each one with different plausible consistency conditions. Heh, but isn`t this offtopic?

I guess the corresponding question in Asymptotic Safety is how many scenarios are there? Do predictions change depending on matter content? Or are there "universal" predictions, eg. spectral dimension (though that alone may not nail down AS, since it is consistent with Horava, if the scalar mode can be fixed). Also, can the spectral dimension be measured - in CDT one of these "dimension" measures was defined with a particle diffusing on a fixed background - isn't this at odds with background independence - so can it be measured with realistic matter content?

 

[MTd2]

There is really no similar situation in asymptotic safety. Asymptotic safety is phase state of certain theories in which all coupling constant are constrained to a finite value. This value is a vector that can span finite dimensional surface, formed by coupling constants which cannot be restrained while transitioning to a low energy scale, like the others are.

 

[atyy]

There is really no similar situation in asymptotic safety. Asymptotic safety is phase state of certain theories in which all coupling constant are constrained to a finite value. This value is a vector that can span finite dimensional surface, formed by coupling constants which cannot be restrained while transitioning to a low energy scale, like the others are.

But they'll need matter to make predictions. I do agree whether pure gravity is safe is an interesting question, but from there to incorporating matter what happens?

 

[MTd2]

Hmmm. Guess what the topic of this thread is about! :) The article should be the answer for your question.

 

[atyy]

(I am aware of the talk about losing dimensionality, but that's more at the level of the space of coupling constants)

I think there are two sorts of losing dimensionality. The first is in the space of coupling constants where the critical surface is finite dimensional (latest number is 3, I think, in Codello's papers). The second is the "anomalous dimension" which is supposed to be 2, I think this is what humanino was thinking about. There's also a "spectral dimension" which seems to be thought of as related to the anomalous dimension, but I'm not sure if that's rigourous - anyway that is supposed to be ~2.

 

[atyy]

Hmmm. Guess what the topic of this thread is about! :) The article should be the answer for your question.

Does Weinberg mention Percacci's GraviGUT?

 

[MTd2]

No, he just lays out a way to do the calculation, in generic terms.

 

[atyy]

No, he just lays out a way to do the calculation, in generic terms.

BTW, did you notice Lubos's comment "Now, you may say that physicists know 5 or 12 or 2009 alternatives to string/M-theory - except that 4 or 11 or 2008 of them already reside at the dumping ground of physics. (http://motls.blogspot.com/2009/10/nature-nyt-report-demise-of-lorentz.html)". This means he thinks that there's currently one reasonable approach other than strings - I'm guessing that's Asymptotic Safety?

 

[Finbar]

"1) There is at least 5 string theories which are conjectured to be all low energy approximations to M-theory."

They are all dual to each other, and hence one theory with one hilbert space (called M theory -- not to be confused with the M theory that is a limit of 11 dimensional SUGRA)

"Classical general relativity where one finds event horizons is the IR approximation to the theory."

The ultra high energy behaviour of quantum gravity is and must be GR again. It becomes classical again at ultra high energy scales, where particle collisions and the (trans) Planckian energy densities simply creates larger and larger black holes (this is called asymptotic darkness). It is this limit that is problematic for a field theory description of gravity, not the IR limit.

So the argument is this: The high energy limit for any consistent field theory (eg not effective), must be asymptotically free or asymptotically safe, and hence scale invariant. The problem (as that paper you linked explains) is you cannot simultaneously be scale invariant, and still describe the classical theory of Einstein gravity (that would be Weyl gravity). So there is a clash.

Your argument just makes no sense its just plainly illogical. If the theory is Asymptotically safe then its not the classical(Einstein Hilbert) theory at the UV fixed point its the conformal theory so there are no black holes. You say "The ultra high energy behavior must be GR again" why? I'm sorry but that's nonsense. In the paper I cited they make no such claim either.

Basically the argument is made by people who don't understand the Wilson. They think that what holds in the IR holds in the UV.

 

[MTd2]

BTW, did you notice Lubos's comment "Now, you may say that physicists know 5 or 12 or 2009 alternatives to string/M-theory - except that 4 or 11 or 2008 of them already reside at the dumping ground of physics.

Only you should only trust him when only he is talking about string, only.

 

[Haelfix]

Your argument just makes no sense its just plainly illogical. If the theory is Asymptotically safe then its not the classical(Einstein Hilbert) theory at the UV fixed point its the conformal theory so there are no black holes. You say "The ultra high energy behavior must be GR again" why? I'm sorry but that's nonsense. In the paper I cited they make no such claim either.

Basically the argument is made by people who don't understand the Wilson. They think that what holds in the IR holds in the UV.

Yea, you seem to miss the point of that paper, b/c that's exactly what it does say. The author is one of Tom Bank's coauthors (whom he thanks at the end of the manuscript), and the original idea goes back to this paper:
hep-th/9812237. Also hep-th/9906038; gr-qc/0201034.

Tom is probably one of three or four people in the world with the best understanding of critical points in high energy physics...

 

[marcus]

But they'll need matter to make predictions. I do agree whether pure gravity is safe is an interesting question, but from there to incorporating matter what happens?

Does Weinberg mention Percacci's GraviGUT?

In line with these questions raised earlier, including matter is evidently critical and we could try to see what the relation is between Weinberg's paper and the recent ones of Percacci.
As far as I know, Percacci (who was the main organizer of the recent AsymSafe conference at Perimeter) is the one who has done the most towards including matter in the asymptotic safety picture. It might help to have the abstracts of his recent papers handy.

As a reminder, so we can carry over some of the understanding gained in the other thread, here is the initial post of the GraviGUT thread:

http://arxiv.org/abs/0910.5167
Gravity from a Particle Physicist's perspective
R. Percacci
Lectures given at the Fifth International School on Field Theory and Gravitation, Cuiaba, Brazil April 20-24 2009. To appear in Proceedings of Science
(Submitted on 27 Oct 2009)
"In these lectures I review the status of gravity from the point of view of the gauge principle and renormalization, the main tools in the toolbox of theoretical particle physics. In the first lecture I start from the old question "in what sense is gravity a gauge theory?" I will reformulate the theory of gravity in a general kinematical setting which highlights the presence of two Goldstone boson-like fields, and the occurrence of a gravitational Higgs phenomenon. The fact that in General Relativity the connection is a derived quantity appears to be a low energy consequence of this Higgs phenomenon. From here it is simple to see how to embed the group of local frame transformations and a Yang Mills group into a larger unifying group, and how the distinction between these groups, and the corresponding interactions, derives from the VEV of an order parameter. I will describe in some detail the fermionic sector of a realistic "GraviGUT" with SO(3,1)\times SO(10) \subset SO(3,11). In the second lecture I will discuss the possibility that the renormalization group flow of gravity has a fixed point with a finite number of attractive directions. This would make the theory well behaved in the ultraviolet, and predictive, in spite of being perturbatively nonrenormalizable. There is by now a significant amount of evidence that this may be the case. There are thus reasons to believe that quantum field theory may eventually prove sufficient to explain the mysteries of gravity."

Garrett's (slightly cryptic) comment was:

Hello PF folk.

If you believe the Dirac equation in curved spacetime, and you believe Spin(10) grand unification, then a Spin(3,11) GraviGUT, acting on one generation of fermions as a 64 spinor, seems... inevitable.

Also, it's pretty.

And it's up to you whether or not to take seriously or not the observation that this whole structure fits in E8. Personally, I take it seriously. Slides are up for a talk I gave at Yale:

http://www.liegroups.org/zuckerman/slides.htmlGarrett

 

[marcus]

More material in line with the questions Atyy raised:

But they'll need matter to make predictions. I do agree whether pure gravity is safe is an interesting question, but from there to incorporating matter what happens?

Does Weinberg mention Percacci's GraviGUT?

I just got the link to Percacci's October 2009 GraviGUT paper. There was a follow-up November paper.

http://arxiv.org/abs/0911.0386
Renormalization Group Flow in Scalar-Tensor Theories. I
Gaurav Narain, Roberto Percacci
18 pages, 10 figures
(Submitted on 2 Nov 2009)

==quote from the conclusions==

Another direction for research is the inclusion of other matter fields. As discussed in the introduction, if asymptotic safety is indeed the answer to the UV issues of quantum field theory, then it will not be enough to establish asymptotic safety of gravity: one will have to establish asymptotic safety for a theory including gravity as well as all the fields that occur in the standard model, and perhaps even other ones that have not yet been discovered. Ideally one would like to have a unified theory of all interactions including gravity, perhaps a GraviGUT along the lines of [45]. More humbly one could start by studying the effect of gravity on the interactions of the standard model or GUTs.

Fortunately, for some important parts of the standard model it is already known that an UV Gaussian FP exists, so the question is whether the coupling to gravity, or some other mechanism, can cure the bad behavior of QED and of the Higgs sector. That this might happen had been speculated long ago [33]; see also [46] for some detailed calculations.

It seems that the existence of a GMFP for all matter interactions would be the simplest solution to this issue. In this picture of asymptotic safety, gravity would be the only effective interaction at sufficiently high scale. The possibility of asymptotic safety in a nonlinearly realized scalar sector has been discussed in [47]. Aside from scalar tensor theories, the effect of gravity has been studied in [48] for gauge couplings and [49] for Yukawa couplings.
==endquote==

The abstract goes right to the cosmology issue, which is likely to be important in establishing (or refuting) asymsafe QG+matter.

==quote from abstract==
We study the renormalization group flow in a class of scalar-tensor theories involving at most two derivatives of the fields. We show in general that minimal coupling is self consistent, in the sense that when the scalar self couplings are switched off, their beta functions also vanish. Complete, explicit beta functions that could be applied to a variety of cosmological models are given in a five parameter truncation of the theory in d=4. In any dimension d>2 we find that the flow has only a "Gaussian Matter" fixed point, where all scalar self interactions vanish but Newton's constant and the cosmological constant are nontrivial... These findings are in accordance with the hypothesis that these theories are asymptotically safe.
==endquote==

 

[Chronos]

I'm just curious where Weinberg is going with this. It appears he has something in mind, be it string, QFD or whatever. String, which cannot be wrong, appears to have limited utility as a predictive tool. On the other hand, renormalization, which cannot be right, has great utility as a predictive tool.

 

[atyy]

I'm just curious where Weinberg is going with this. It appears he has something in mind, be it string, QFD or whatever. String, which cannot be wrong, appears to have limited utility as a predictive tool. On the other hand, renormalization, which cannot be right, has great utility as a predictive tool.

In fact renormalization is key. Renormalization says that our current theories are only low energy effective theories, and gives us two broad classes of options for the high energy theory. The first class is that the high energy theory contains the same symmetries and degrees of freedom as the low energy theory - this is asymptotic safety. The second class is that the high energy theory contains very different symmetries and degrees of freedom - this is called unification in high energy physics, or emergence in condensed matter physics, where for example, phonons are degrees of freedom at low energy that emerge from vastly different degrees of freedom at high energy. The second class of theories is presumably vaster (though it seems string theory is the only known member of this class so far), since many different high energy theories could flow to the same low energy theory, which is why they say the renormalization group is a semigroup. However, in the first class, the renormalization group can in principle be reversed since the degrees of freedom are the same, and this is the Asymptotic Safety scenario - or scenarios, since there may be more than one way to include matter.

 

[Finbar]

Yea, you seem to miss the point of that paper, b/c that's exactly what it does say. The author is one of Tom Bank's coauthors (whom he thanks at the end of the manuscript), and the original idea goes back to this paper:
hep-th/9812237. Also hep-th/9906038; gr-qc/0201034.

Tom is probably one of three or four people in the world with the best understanding of critical points in high energy physics...

The paper does't say anywhere that the action in the UV will be Einstein-Hilbert. We know its Einstein-Hilbert in the IR but it certainly not in the UV. Their argument is based on the IR scaling being different from the UV. But this is fine because the scaling will change as we flow from the IR to the UV. In the conclusion they say

"We believe this counter-argument does not hold because the asymptotic safety scenario is based on the assumption that gravity is a valid low energy approximation to some putative local quantum field theory. Therefore at least in its regime of validity it should be trusted. In particular it should be trusted to describe the horizons of large black holes, since as can be seen from Eq. 31 the more massive a black hole is, the lower is the curvature at the horizon."

But if the curvature is low then we are still in the Einstein Hilbert low energy regime so I don't expect the scaling to be conformal. Its only when the curvature is high that we approach the fixed point and the scaling should be conformal. Thus we approach the high energy regime only for a Planck sized black hole.

Either their black hole argument is correct and gravity cannot be described as a QFT or there is a logical inconsistency in their argument in there argument and gravity can be described by a QFT. I've pointed out the logical inconsistency and I think its pain to see if you look a little beyond the surface of their papers.

In the end though I think their papers are good because they really give a physical meaning to Asymptotically safe gravity. That is any asymptotically safe theory of gravity should not contain black holes in the Planck regime.

 

[marcus]

I'm just curious where Weinberg is going with this. ... renormalization, which cannot be right, has great utility as a predictive tool.

In fact renormalization is key. Renormalization says that our current theories are only low energy effective theories, and gives us two broad classes of options for the high energy theory. The first class is that the high energy theory contains the same symmetries and degrees of freedom as the low energy theory - this is asymptotic safety. The second class is that the high energy theory contains very different symmetries and degrees of freedom - this is called unification in high energy physics, or emergence in condensed matter physics, where for example, phonons are degrees of freedom at low energy that emerge from vastly different degrees of freedom at high energy. The second class of theories is presumably vaster (though it seems string theory is the only known member of this class so far), since many different high energy theories could flow to the same low energy theory, which is why they say the renormalization group is a semigroup. However, in the first class, the renormalization group can in principle be reversed since the degrees of freedom are the same, and this is the Asymptotic Safety scenario - or scenarios, since there may be more than one way to include matter.

Good question and what I think is a valuable concise answer---one I want to carry along because this exchange seems essential to the thread.
Chronos to get more of an idea where S.W. is going, what he has in mind, you could watch his 6 July video. It presents an overarching vision of where things are going in high energy physics. The pendulum swinging back to field theory and the 1970s Wilsonian renormalization approach. Scale dependence of the constants you plug into the theory is really "how the world is". He says "I don't want to discourage anyone from working in string theory, but it might turn out that string theory is not needed. It might not be how the world is."

That talk seems to have upset a lot of people. It was the opening talk of a CERN conference on the state and prospects of high energy physics, with a large audience including a lot of string theorists. The paper that later came out from that talk was considerably toned down and left out good stuff where he gave an overview of the growth of quantum field theory since the 1920s. One of his slides sketched cyclic waves of theoretician's fashion that have resulted in a kind of staircase rise. Field theory as he depicted it, has periods of rapid advance that encounter problems which then lead to a temporary lull during which radical alternatives are tried and don't work out. Then after that plateau period, field theory has (historically at least) had another surge and has risen to the next plateau.

He wasn't claiming to know the future--the tone was very modest. In effect saying " This is just how I see it. This is why I'm working on asymptotic safe (with the cosmology application) now."
Well you asked what does he have in mind. You asked where is he going with this. That talk is the most explicit answer I know. It presents an overarching vision of the past 80 years or so of high energy physics and where he thinks its going and how renormalization fixed points fit into that.

One thing that impressed me is how gentle and unarrogant. He is skillful at speaking carefully, with correctly qualified statements, without seeming pedantic. Nice low-pressure personality. The first 57 minutes are a historical overview--then he starts discussing his current research interest and explaining why this particular track.

 

[marcus]

About the idea that "renormalization cannot be right"----which I think was part of a tongue-in-cheek witticism---that raises the interesting question of why the world seems to work that way. The Perimeter Asymptotic Safety conference had several papers offering mechanisms to explain the flow of parameters with scale.

Atyy gave a concise account. In much of field theory you keep the same formula, you just gradually change the parameters you plug into it.

The "form of the Lagrangian" remains the same, but its coupling constants "run" as the relevant energy ramps up, or as you zoom the microscope in.

And the basic formula of the theory can have symmetries at high energy which disappear as the energy declines. That is, there can be terms in the basic formula which are negligible at one scale (and therefore do not disturb the symmetry) but which become large and significant at another scale.

Well this can be so unintuitive to you that your reaction is it must be all bunk and hokum.
But give Steven Weinberg a break! He is a nice guy and experienced and wise. And a lot of people find the running of constants with scale to be actually intuitive! It makes sense to them that nature should behave that way! We have to be tolerant of each other. We have different attitudes about certain things.

Personally I like running constants a lot. And also what is called "shielding and antishielding". How forces can change depending on the vacuum in between. The role that the vacuum plays. And I have glimmerings of intuition about how running constants could arise in nature. Interesting mechanisms explaining it have been offered. My attitude is that the renormalization group flow, that modifies constants with scale, is actually not hokum, or a dishonorable kludge (which you might think) but is elegant, and economical. The idea that you can make do with a single formula (if it is the right one) just by letting the constants run.

Anyway, have another look at Atyy's brief summary and see if you can look at things more from Weinberg's perspective. And remember his CERN talk caused a lot of nervous upset denial and clamor, which is real nice to hear and enjoyable to listen to.
If you want the video it is here:
http://cdsweb.cern.ch/record/1188567/

 

[atyy]

Atyy gave a concise account. In much of field theory you keep the same formula, you just gradually change the parameters you plug into it.

The "form of the Lagrangian" remains the same, but its coupling constants "run" as the relevant energy ramps up, or as you zoom the microscope in.

A reference that I've found very useful is Kardar's statistical mechanics notes. In his exposition, we start with all possible terms having the symmetries we know of experimentally (http://ocw.mit.edu/NR/rdonlyres/Physics/8-334Spring-2008/7507574B-4ADC-4611-8058-5985074514A8/0/lec7.pdf ) - because "We also discovered that even if some of these terms are left out of the original Hamiltonian,they are generated under coarse graining (http://ocw.mit.edu/NR/rdonlyres/Physics/8-334Spring-2008/109D498F-09AA-4503-ACFB-C9657CF2B157/0/lec12.pdf )." - in other words, the calculations show that the coupling constants run as you zoom the microscope out.

Although this is statistical mechanics, not quantum field theory, Weinberg's Asymptotic Safety proposal resulted from him trying to learn statistical field theory. http://ccdb4fs.kek.jp/cgi-bin/img/allpdf?197610218

 

[Finbar]

It troubles me slightly that people still seem unsure as to whether couplings run or whether the renormalisation group is physical. These are well tested facts and Kenneth Wilson was awarded the Noble prize for his work on the renormalisation group.

I would go as far as saying that if you don't understand the renormalisation group you don't understand QFT. Sure you can mindlessly compute scattering amplitudes computing Feynman diagrams but this only tells you stuff about scattering phenomena in some man made experiment. Real physics like the confinement of quarks needs a full non-perturbabtive understanding of QFT which we still lack. Our best tools to approach these problems come from the lattice and renormalisation group techniques.

 

[friend]

The "form of the Lagrangian" remains the same, but its coupling constants "run" as the relevant energy ramps up, or as you zoom the microscope in.

Aren't mass and charge also compling constants. Do you mean that these can change with scale? I don't know any reason why they shouldn't change.

If the "constants" change, then does this just make them another kind of field in QFT? Or are the parameters that change the "constants" not the same as the spacetime coordinates of QFT? You did mention scale which depends on spacetime coordinates.

 

[atyy]

Aren't mass and charge also compling constants. Do you mean that these can change with scale? I don't know any reason why they shouldn't change.

If the "constants" change, then does this just make them another kind of field in QFT? Or are the parameters that change the "constants" not the same as the spacetime coordinates of QFT? You did mention scale which depends on spacetime coordinates.

Let's say you have a theory in which fundamentally everything is a bunch of classical point masses connected by classical springs with spring constant k. But if you cannot experimentally manipulate neighbouring points (high energy or small scale), and can only manipulate far away points (low energy or large scale), then you will get some effective spring constant spring constant k' when you treat the multiple in between springs as one spring, so the coupling constant will run with energy or scale.

http://en.wikipedia.org/wiki/Hooke's_law

 

[marcus]

Aren't mass and charge also compling constants. Do you mean that these can change with scale? I don't know any reason why they shouldn't change.

If the "constants" change, then does this just make them another kind of field in QFT? Or are the parameters that change the "constants" not the same as the spacetime coordinates of QFT? You did mention scale which depends on spacetime coordinates.

The constant (say a mass) is constant through-out space and time. It does not depend on the coordinates. It only depends on the scale---which can be an energy or scale of spatial resolution.

Imagine looking at the whole process at one scale, and then look again at a closer scale, as with a zoom microscope. Or photographing a motion picture with finer and finer pixels.

You have probably heard of the "bare" mass of a particle as contrasted to the mass measured at low energy and macroscopic distance.

You probably know that in QED (quantum electrodynamics) there is this important number which is NOT always 1/137. That is only the macroscopic low energy value, for when the two electrons never get very close to each other. If you increase the energy of the collision, or decrease the distance scale of the encounter, then the correct number gets larger, like 1/135, or 1/133.

None of this variation depends on spacetime coordinates, it does not vary with position. It varies only with the degree of coarseness or refinement with which one is viewing the process. Alternatively, the characteristic energy of an interaction. Because if you fire two things at each other with more energy, they get closer. Energy and length are in an inverse relation.

 

[friend]

None of this variation depends on spacetime coordinates, it does not vary with position. It varies only with the degree of coarseness or refinement with which one is viewing the process.

The only way I can (presently) imagine this is if, say, the interval of integration in the path integral changes from minus to plus infinity to something smaller. Then I can understand how the coupling constants would change. Is this what's going on?

 

[marcus]

The only way I can (presently) imagine this is if, say, the interval of integration in the path integral changes from minus to plus infinity to something smaller. Then I can understand how the coupling constants would change. Is this what's going on?

You can ask Finbar or Atyy to explain it more rigorously. To me this "scale" is an embryonic idea which is growing in the mind of physics and which has already shown enormous practical validity, so that it must correspond to something real---which however is as yet not fully defined. It dates from the seminal work of Ken Wilson in the 1970s (But Atyy traces the idea back further in other kinds of physics, not particle.) And just two weeks ago at the Perimeter conference, Vincent Rivasseau presented a different way to think about scale and a different reasoning about how things run with scale. So I think of it as ongoing work in progress, how we think about this.

Let's see if we can find something about the running of the fine structure constant. I couldn't find anything in Wikipedia the first time I tried but I found a study that said that the value could get as high as 1/128.96.
So roughly the fine structure constant at very high energies is around 1/129, instead of 1/137. Maybe somebody else has a good source for this.

 

[atyy]

The only way I can (presently) imagine this is if, say, the interval of integration in the path integral changes from minus to plus infinity to something smaller. Then I can understand how the coupling constants would change. Is this what's going on?

Yes. Take a look at Eq (A.1) and (A.2) of http://relativity.livingreviews.org/Articles/lrr-2006-5/ . The LHS of (A.1) is taken over everything less than Lambda, while the RHS is taken over everything less than (Lamda-dl), because you coarse grained over dl as defined in (A.2).

You may also find useful Hollowood's notes about how the usual bizarre description of renormalization is related to Wilsonian common sense. http://arxiv.org/abs/0909.0859

 

[friend]

Yes. Take a look at Eq (A.1) and (A.2) of http://relativity.livingreviews.org/Articles/lrr-2006-5/ . The LHS of (A.1) is taken over everything less than Lambda, while the RHS is taken over everything less than (Lamda-dl), because you coarse grained over dl as defined in (A.2).

So you're saying the constants change because of coarse graining the integration variables? Or is there more to it than that? Thanks.

 

[atyy]

So you're saying the constants change because of coarse graining the integration variable? Or is there more to it than that? Thanks.

That's all. Very simple conceptually, but very demanding technically.