Nonperturbative QG: the emerging theory

[marcus]

I notice that Loll calls what she does "nonperturbative quantum theory of gravity" and she calls CDT (which she and several others developed) a METHOD to do nonperturbative QG with.

And the organizers of this years conference Loop 05 say it is the annual conference of researchers in "nonperturbative/background independent" quantum gravity.

http://loops05.aei.mpg.de/

And at the conference they have people basically united by a common goal, all trying to discover or build the same theory, but using various methods:

CDT
spin foams
other kinds of path integrals
canonical LQG
causal sets
...
...

So I am beginning to try to see this as a single emerging theory where there is pretty good agreement about what it should do (classical limit is Gen Rel, quantum theory of spacetime geometry, quantum spacetime dynamics, maybe include topological variation).

Of course I am not an expert and I don't have this as clearly in mind as I would like, but I sense that these people understand each other's concerns and methods and aims, and they are engaged in trying various methods towards a common purpose. And often encountering analogous problems. Getting experience one place that will apply somewhere else. And I see often the same person will try several lines of research. So the Loop 05 conference is not a gathering of several separate competing ball teams, with sharp lines allegiance drawn. It is looking like a single non-partisan workforce all working by various schemes to bring to light the same theory.

Sideline observers (like myself) can probably at this point form some mental pictures of how the nonperturbative QG theory is going to turn out and they may not be too far wrong, if we are careful.
I get my mental imagery of QG largely from Loll's CDT, but I have a strong suspicion that WHATEVER the formalism and methods that might eventually be used and might replace causal dynamical triangulation methods, what comes out will likely be at least ANALOGOUS to what I can see now.

For example it will have to start out with no spacetime shape at all, and introduce a MICROSCOPIC DYNAMICAL PRINCIPLE that operates at small scale and (as its influence expands outwards) generates largescale spacetime geometry behavior matching Einstein Gen Rel. And this microscopic operating principle is going to have to generate a world that appears 4D at large scale (but may have different behavior down small scale) and thus it must EXPLAIN why we have macroscopic 4D spacetime.

And the theory will have to be able to generate the myriad quantum possibilities of geometry----all differerent shapes of the 4D continuum---and provide a place for matter particles to run around in or for matter fields to ripple around in----and provide some mechanism for the matter and the spacetime geometry to interact.

And it will have to get rid of the Big Bang singularity, and see what is beyond the classical theory breakdown. And the Black Hole singularity.
Because the examples of CDT and LQC show us that is the kind of thing that QG theories do: they smooth over classical singularities. And, following the example of LQC it should provide a natural generic mechanism for inflation---so we don't need a gimmick.

So what we are seeing now, and what people will talk about at Loop 05, in October, is teaching us WHAT TO EXPECT of a nonperturbative QG theory, and what things to look for as one gradually rises out of the swamps of our curiosity and confusion.

And we can probably use a thread, like this, to be about the dim emerging shape of nonperturbative QG, from the glimpses we can get in its various current formats.

 

[Chronos]

Perturbative QG might also still be in play:
http://www.arxiv.org/abs/gr-qc/0311082
Quantum Gravity in Everyday Life: General Relativity as an Effective Field Theory

 

[marcus]

Perturbative QG might also still be in play:
http://www.arxiv.org/abs/gr-qc/0311082
Quantum Gravity in Everyday Life: General Relativity as an Effective Field Theory

hello Chronos, I have been reading the CP Burgess paper you mentioned for a while this morning, this time on your suggestion. Not the first time i looked at it. Each time I return I see things a little more clearly, if only because more in context.

I don't see per and nonper QG as replacements for each other----for the most part they seem good for different things. I assume you also don't consider Burgess QG as fulfilling the same purpose as the nonperturbative QG people are trying to construct. Still good to keep in mind that Burgess approach is there.

I'd be interested in how you characterize the difference betw. per and nonper approaches. this AJL paper (hep-th/0505154) begins:

<<Nonperturbative quantum gravity can be defined as the quest for uncovering the true dynamical degrees of freedom of spacetime geometry at the very shortest scales. Because of the enormous quantum fluctuations predicted by the uncertainty relations, geometry near the Planck scale will be extremely rugged and nonclassical. Although different approaches to quantizing gravity do not agree on the precise nature of these fundamental excitations, or on how they can be determined, most of the popular formulations agree that they are neither the smooth metrics g_mu, nu (x) (or equivalent classical field variables) of general relativity nor straightforward quantum analogues thereof. In such scenarios, one expects the metric to re-emerge as an appropriate description of spacetime geometry only at larger scales. >>

Perturbative QG starts with a fixed smooth metric, often simply flat, that approximates the macroscopic world we see. And it then sets out one or a few massive particles and studies by successive finer and finer approximation how they perturb the smooth background metric.

This appeals to me as pragmatic and commonsense. I wouldn't expect it to apply in highly curved or extreme dynamic situations like around the big bang or during gravitational collapse. I would not expect to ever be able to learn about the fundamental degrees of freedom, if that is possible, or the actual mechanism by which matter couples to geometry. Or to discover, from that practical commonsense analysis, some way in which matter is reprepresented as a feature of geometry itself. But it is admittedly ambitious, perhaps quixotic, to want deeper, more fundamental explanations.

By contrast, nonper QG does not start with any prior background metric at all! No background smooth or unsmooth. It seeks a fundamental microscopically-operating dynamic rule from which the geometric behavior of spacetime grows and from which the observed macroscopic behavior can naturally develop. I think of nonperturbative QG as a more ambitious project which does not at all compete with the Burgess program you cited. I think of Burgess program as more aimed at getting a workable approximative theory with some quantum corrections that somebody can calculate.

Didnt mean to talk so much. I started thinking i would inquire how you saw the per/non per difference and then slid into expounding my own viewpoint
Any reactions?

[EDIT: hi Chronos, responding to the following post. Thanks for the references. I'll have a look as time permits.]

 

[Chronos]

Marcus, your summation is quite correct by my loosely constructed understanding of the literature. To paraphrase Smolin - non-perturbative theory must have a good classical limit which reduces to a consistent and stable perturbative theory. Having a sound perturbative theory is crucial, in my mind, to the ability to test any candidate non-perturbative model. While the quantum corrections in perturbative theory are quite small, they should be reproduced by the correct np-model. So, basically [again in my mind] perturbative QG is to non-perturbative QG as SR is to GR.

Here is another food for thought entre where PQG may drop clues to where the correct NQG model is hiding:

http://lanl.arxiv.org/abs/gr-qc/0206071
Perturbative Quantum Gravity and its Relation to Gauge Theory
Author: Zvi Bern

Unsurprisingly this paper was cited in the Burgess paper, as well as here:

http://lanl.arxiv.org/abs/gr-qc/0404122
The Chrono'Geometrical Structure of Special and General Relativity: Towards a Background-Independent Description of the Gravitational Field and Elementary Particles
Authors: Luca Lusanna (INFN, Firenze)

where the author makes an interesting bid to unite the realms. Having a penchant for tracing the lineage of important papers [like AJL's http://arxiv.org/hep-th/0505154] [Broken] can lead to some odd places. It is fascinating [albeit time consuming] to see how the pieces come together [and sometimes apart].

 

[marcus]

What to call it, "Quantum Spacetime Dynamics"? or just plain "QG"

Gravity is handled perturbatively in string theory.
String is the main example of perturbative quantum gravity approach. I guess there are a bunch of others, Chronos you have mentioned some. but the main one is String

So when Renate Loll calls what she does "nonper" QG, what she is primarily signaling is that it is NON-STRING.
If she didnt have this 500 pound gorilla competition at her elbow, she would simply say "quantum gravity".

And when the organizers of the Loop 05 say "this conf. is not limited to Loop, it is to include all "non-perturbative/background independent" quantum gravity approaches, what they would like to say is this is simply the conference on Quantum Gravity. because of course authentic QG has to be NP/BI because Einstein Gen Rel is NP/BI. but they can't because they have this perturbative background DEpendent rival, so they need a codeword for NON-STRING.

The nonper QG approaches are in the APPLE/MICROSOFT relation to string. They must always be worried about being engulfed by this huge amoeba.
So they struggle to distinguish what they do, and put non-string stamps on it so that it can't be taken over and declared a bastard brain-child of Edward Witten or some other goshawful thing.

 

[selfAdjoint]

So when Renate Loll calls what she does "nonper" QG, what she is primarily signaling is that it is NON-STRING.

Oh I don't think so. all the Ashtekar-Rovelli-Baez wing of quantum gravity - the "LQG" wing - is perturbative. Loll is not trying to distance herself from strings, she is genuinely proud of a non-perturbative breakthrough in a field which has longed for just that since it began back in the days of De-Witt.

 

[marcus]

"Nonperturbative" is a clumsy word

People at PF, many at least, have a good ear for language and can tell that nonperturbative is an awkward word.

It has no visual content (no image icon comes to mind) and it has 5 syllables, and moreover it is a negative.

One thing I like about Renate Loll is she ordinarily writes good English (not just for a native Germanspeaker but for anybody). May be it was studying at London Imperial or it may just be a sign of an extra good mind, but she writes real English. And she chooses to say that her goal is to build a Nonper. QG theory and that CDT, which she developed with Ambjorn, is a METHOD, in other words one possible method for doing Nonperturbative Quantum Gravity.

OK Renate, you are in charge and you choose the words. You want to say that your goal, and that of Smolin, Rovelli, Freidel and all the others, is a "Nonperturbative Quantum Gravity".
Let's listen to how it sounds. Here is the abstract of your recent landmark paper, "Reconstructing"

"We provide detailed evidence for the claim that nonperturbative quantum gravity, defined through state sums of causal triangulated geometries, possesses a large-scale limit in which the dimension of spacetime is four and the dynamics of the volume of the universe behaves semiclassically. This is a first step in reconstructing the universe from a dynamical principle at the Planck scale, and at the same time provides a nontrivial consistency check of the method of causal dynamical triangulations. A closer look at the quantum geometry reveals a number of highly nonclassical aspects, including a dynamical reduction of spacetime to two dimensions on short scales and a fractal structure of slices of constant time."

Notice that in her words the theory is Nonper QG and that it is DEFINED THROUGH a certain method which is "state sums of causal triangulated geometries"---another way of saying the CDT path integral, a quantum superposition of all possible geometries of a certain kind.

But Richard NC, for instance, does not warm to the word "nonperturbative". Let's try alternatives. It is not an easy English-style problem. Let's try "quantum spacetime dynamics"

"We provide detailed evidence for the claim that quantum spacetime dynamics, defined through state sums of causal triangulated geometries, possesses a large-scale limit in which the dimension of spacetime is four and the the volume of the universe behaves semiclassically..."

well, have to think about it. Anybody like the sound better?

 

[marcus]

Oh I don't think so. all the Ashtekar-Rovelli-Baez wing of quantum gravity - the "LQG" wing - is perturbative. Loll is not trying to distance herself from strings, she is genuinely proud of a non-perturbative breakthrough in a field which has longed for just that since it began back in the days of De-Witt.

selfAdjoint! delighted to have someone else in the discussion. I was feeling like I was talking to myself, or to an imaginary Renate Loll

glad you are concerned with these language matters too, in the longrun the words do matter don't they.

 

[marcus]

why we should understand nonpertubativeness as an idea

I just reviewed the situation, looked over some abstracts and some papers, and I think that at least for the present we can't get around the need for this word "nonperturbative" which may have unclear, or little meaning to many of us.

It is too important and too central in the discussion for us to try to avoid it so we will just have to make an effort to infuse some meaning into it and get used to it---ugly 5-syllable sucker that it is.

as selfAdjoint says a couple of posts back, nonperturbativeness has been a longstanding ideal or goal to strive for or dream.

I'm going to show some other places the concept comes up, to indicate how central it is in the quantum gravity business.

for example here's Peter Woit quoting Larry Yaffe, the person who alerted Ed Witten to some 1984 string developments and so was around at the early days of the field.

http://www.math.columbia.edu/~woit/blog/archives/000069.html
----quote from Woit---
Jeff Harvey's comment that it was Larry Yaffe who brought news of the Green-Schwarz anomaly cancellation result to Witten gave me the idea of contacting Larry to get a first-hand recollection of what the reaction was at Aspen back in 1984. He was a junior faculty member at Princeton at the time...

"Since you asked about my views on string theory, I'll try to give a summary. I think it is clear that:

String theory has been wildly over-hyped by some people. Even calling it a 'theory' is really a misnomer, given the lack of any adequate non-perturbative definition of string theory.

String theory has not yet made any convincing connection with the world we live in.

The predictive power (or the falsifiability) of string theory leaves much to be desired, especially in light of the emerging picture of the landscape of string theory vacua.

But at the same time:

The oft-repeated argument that string theory is the most promising framework we have for combining quantum mechanics and gravity remains true. Even though there is no real non-perturbative definition of string theory, I don't think one can dispute this assertion..."

---end quote---

Now I disagree with Yaffe, as it happens. I don't think it is at all clear that "string theory is the most promising framework we have for combining quantum mechanics and gravity". I would cite Loll and coworker's advances towards a nonperturbative path integral---work that has come out in the past year. But that is not the point.

The point I want to make with this quote from Yaffe is the importance he places on the idea that a fundamental gravity theory should non-perturbative

This is the make-or-break feature for Yaffe (in common with a lot of other theoretical physicists) or so it would seem. That is why I think we should study this concept and try to get at the essence of it.

 

[marcus]

What does nonperturbative mean and what's an example?

Well a perturbative way of solving a problem is to start with an answer already---maybe an answer to a simpler problem (with some complication left out) and then consider how to solve it with that complication included and you say

new solution = old solution + a little change or perturbation.

and you can set up an equation to solve for what the little change has to be.

So imagine you are teaching children how to write stories and you say "Write a story about how, a long time ago, a Chinese girl saved her city". That is giving the problem NONperturbatively and they may have trouble thinking of how to do it.

Then you make it a perturbative problem, you actually GIVE them a solution to a similar problem---the little Dutch boy with his finger in the dike---and have them read that. And then you say "ADAPT this so that it is a little Chinese boy!" Of course they will wonder if there are dikes in China and you say yes there are plenty of dikes in China. So they write the story and then you say "Change this so that it is a little Chinese girl instead!" And each time they have to think about how to perturb it.

There is a series of finer and finer changes that they make to do the perturbation. The Dutch boy eats his muesli for breakfast with a spoon and puts on his wooden shoes and goes out to play. That all gets changed so the Chinese boy eats his breakfast riceballs with chopsticks and maybe instead of wooden shoes puts on his cloth slippers. These are called first order differences. And when the solution gets perturbed further so it is a girl, then the pronouns all have to get changed. that is also a first order difference. and then there will be second order, finer more subtle differences, probably, which you can think of. Like, because she is a girl does she think different thoughts or play different games. does she have different responsibilities that she is neglecting at home because she stays with her finger in the dike. Does a different person come looking for her after a long time, that evening? And so on. these are second order, third order fourth order changes and they get less and less crucial. the important changes are the first order, like change the pronouns dummy!

The thing about perturbative is you get handed a solution to start with that you can gradually modify to suit different conditions, as long as the new conditions arent too different. It is not a panacea because there's a limit to how much you can adapt a given pattern to new situations before something snaps or goes haywire.

The thing about nonperturbative is you don't get handed a readymade solution. You have to make up your solution FROM SCRATCH or pull it out of thin air.

That is what I like so much about Loll's spacetime continuum. She doesn't start with somebody's old differentiable manifold. She doesn't take somebody's well-worn readymade continuum and perturb it or tinker with it. She starts from no prior and creates spacetime afresh. And it comes out surprising in ways nobody specifically thought of asking for.

 

[Chronos]

Marcus, it won't be easy to find even a string theorist to argue background independence is not a desirable, or even necessary element of any properly conceived theory of quantum gravity. While a non-perturbative version of string has not been achieved [nor has it been easy to do using any other approach], it's not for lack of interest [don't take that as an endorsement of ST]. At the same time, dismissing ST out of hand is no more sensible than rejecting loop and CDT because they are not part of ST. I like the approach by Smolin and Thiemann, who have, IMO, lead an effort to bring all the approaches to quantum GR together and following the bread crumb trails that emerge. It seems like a reasonable approach - Put the ego's aside and worry about the awards ceremony AFTER the goal has been achieved. The mythological TOE can wait, a quantum GR is the most pressing need and we should apply every useful, available tool to that effort. With your indulgence, a couple of papers I think are important examples of right-headedness [and suggest I'm a closet supporter of Smolin for 'the next Einstein' award].

Strings as perturbations of evolving spin-networks
http://xxx.lanl.gov/abs/hep-th/9801022

To me, this innocuous looking work is a 'paper of the century' candidate. And Smolin probably saved ST with this pivotal followup paper:

http://www.arxiv.org/abs/hep-th/0401172
Title: Scientific alternatives to the anthropic principle
Authors: Lee Smolin

I'm sure you are well acquainted with all these works, marcus, but it might be useful for others trying to weave their way through the morass of historical progression. I'm also very intrigued by the works of Thiemann, in particular this paper:

http://www.arxiv.org/abs/hep-th/0401172
The LQG -- String: Loop Quantum Gravity Quantization of String Theory I. Flat Target Space
Authors: Thomas Thiemann

And it's not the result that's so important, it's the approach and, IMO, the right way to do science in the face of adversity. Thiemann took some hits for that one. He'd have had a better chance of sneaking a gravy boat past a junk yard dog.

 

[marcus]

What does nonperturbative mean and what's an example?

Well a perturbative way of solving a problem is to start with an answer already---maybe an answer to a simpler problem (with some complication left out) and then consider how to solve it with that complication included and you say

new solution = old solution + a little change or perturbation.

and you can set up an equation to solve for what the little change has to be.

...

The thing about perturbative is you get handed a solution to start with that you can gradually modify to suit different conditions, as long as the new conditions arent too different. It is not a panacea because there's a limit to how much you can adapt a given pattern to new situations before something snaps or goes haywire.

The thing about nonperturbative is you don't get handed a readymade solution. You have to make up your solution FROM SCRATCH or pull it out of thin air.
...

What I'm working on in this thread right now is an understanding of the idea of nonperturbative especially for an interested layman.

I want to touch on the mathematical definition, as well as the intuitive notion, and the importance that physicists give to it as a feature of a physical theory.

Here is the WIKI definition of PERTURBATION THEORY (general math context)

http://en.wikipedia.org/wiki/Perturbation_theory


"Perturbation theory comprises mathematical methods that are used to find an approximate solution to a problem which cannot be solved exactly, by starting from the exact solution of a related problem. Perturbation theory is applicable if the problem at hand can be formulated by adding a "small" term to the mathematical description of the exactly solvable problem. Perturbation theory leads to an expression for the desired solution in terms of a power series in some "small" parameter that quantifies the deviation from the exactly solvable problem. The leading term in this power series is the solution of the exactly solvable problem, while further terms describe the deviation in the solution, due to the deviation from the initial problem. Formally, we have for the approximation to the full solution A a series in the small parameter (here called epsilon), like the following:"

Maybe you can see here the analogy with with story of the little Chinese girl with her finger in the dike.

Essential thing is "to find an approximate solution to a problem which cannot be solved exactly, by starting from the exact solution of a related problem." You resort to it if you can't set the problem up in a way that let's you get an exact solution. If the basic problem is too hard, then solve a simpler problem and see if you can gradually modify and adapt the solution to the easy problem.

WIKI also has a page discussing Perturbation Theory in a physics (Quantum Mechanics) context.

http://en.wikipedia.org/wiki/Perturbative

The Wiki math context definition, the first link, is actually pretty nice IMO and it shows how you can get a PERTURBATION SERIES by an iterative proceedure of solving for the correction term step by step to higher and higher "order".
I'd say it is worth looking at just to get the flavor even if you don't usually do math.
After glancing at the math context definition, if you look at the applied-to-physics definition (the second link) you will see the same things going on but in quantum mechanics garb, just dressed up in slightly different clothes.

 

[Mike2]

What I'm working on in this thread right now is an understanding of the idea of nonperturbative especially for an interested layman.

I want to touch on the mathematical definition, as well as the intuitive notion, and the importance that physicists give to it as a feature of a physical theory.

So one thing you might ask yourself in regards to perturbative v. non-perturbaitve Quantum Gravity is whether perturbative solutions are background dependent and whether non-perturbative is background independent. For it might be that the series solution involve a differential change which may be with respect to an assumed background. What do you think?

 

[selfAdjoint]

So one thing you might ask yourself in regards to perturbative v. non-perturbaitve Quantum Gravity is whether perturbative solutions are background dependent and whether non-perturbative is background independent. For it might be that the series solution involve a differential change which may be with respect to an assumed background. What do you think?

Well LQG is a perturbative theory that is background free, and CDT is a nonperturbative theory that is background free, whilte the Standard Model is a perturbative theory which is background dependent while M-theory is a non-perturbative theory that is background dependent. So the proposed link between background dep/indep and pert/non-pert doesn't seem to hold up.

 

[marcus]

I have been reading a range of articles that discuss either perturbative or nonperturbative theories, to get a handle on why nonperturbativeness is so valued

What i pick up is that a perturbative theory or method is approximative

and by contrast a nonperturbative solution or method is (whether or not the word is used as a synonym) EXACT.

The sense I get from reading (I can supply links later, esp. if desired) is that if it is possible to get a nonpert, or "exact" unapproximative theory then one should go after it because it is more likely to reveal the the true degrees of freedom of what is being studied. But if it is NOT possible to get an exact theory then one is happy to make do with an approximative perturbation theory. (again, if one can manage to get even that).

So, although they seem rarely to come out and say it directly, there is a subtle NUANCE or connotation of "exact" or "true" riding along with this word "nonperturbative". It seems to explain the value physicists appear to place on getting a nonpert. theory wherever it turns out to be practical to do so.

=========EDIT ON LATER========
as an experiment with language, let's try "exact" in the sense of non-approximative, in place of "nonperturbative" in the summary Loll gives of the recent paper Reconstructing the Universe:

"We provide detailed evidence for the claim that exact quantum gravity, defined through state sums of causal triangulated geometries, possesses a large-scale limit in which the dimension of spacetime is four and the dynamics of the volume of the universe behaves semiclassically. This is a first step in reconstructing the universe from a dynamical principle at the Planck scale, and at the same time provides a nontrivial consistency check of the method of causal dynamical triangulations. A closer look at the quantum geometry reveals a number of highly nonclassical aspects, including a dynamical reduction of spacetime to two dimensions on short scales and a fractal structure of slices of constant time."

 

[marcus]

I want to try another substitution. In this paper http://arxiv.org/hep-th/0505154 [Broken]
the first paragraph starts out this way:

"Nonperturbative quantum gravity can be defined as the quest for uncovering the true dynamical degrees of freedom of spacetime geometry at the very shortest scales. Because of the enormous quantum fluctuations predicted by the uncertainty relations, geometry near the Planck scale will be extremely rugged and nonclassical..."

Let's try it with exact (using exact as the opposite of perturbative)

"Exact quantum gravity can be defined as the quest for uncovering the true dynamical degrees of freedom of spacetime geometry at the very shortest scales. Because of the enormous quantum fluctuations predicted by the uncertainty relations, geometry near the Planck scale will be extremely rugged and nonclassical..."

There is a slight misintention in the original, what she really means to say, I suppose, is that THE ATTEMPT TO WORK OUT A nonperturbative theory of quantum gravity can be defined as the quest for uncovering the true dynamical degrees of freedom of spacetime geometry..."

So if we think of exact as the opposite of approximative, then in those terms what she is talking about is the quest for exact quantum gravity.

Maybe now the words convey the right sense: the quest for an exact quantum theory of gravity or of spacetime.

 

[selfAdjoint]

Perturbative methods can only be used in weak field cases. The field is treated as a perturbation, or SLIGHT modification of the free no-field case. Then the results can be expanded in powers of the coupling constant, and as long as the interaction stays weak, the series will converge, or at least be something usable for a few terms.

By contrast non-perturbative methods can dig in where the fields are strong. In many cases the perturbative methods are too difficult to use against a continuum background so an approximation is used. Non-perturbative methods in high energy particle physics are almost all done on the lattice, and we find the non-perturnative CDT quantum gravity using their triangulations.

It is the fate of people who study real differential equations, rather than school book examples, to do approximations. The limited number of special cases that can be solved exactly form a study by themselves, and have their own little section of the arXiv devoted to them. So approximate versus exact is not the line that separates perturbative from non-perturbative; it is strong field interactions versus weak ones.

 

[marcus]

Perturbative methods can only be used in weak field cases. The field is treated as a perturbation, or SLIGHT modification of the free no-field case. Then the results can be expanded in powers of the coupling constant, and as long as the interaction stays weak, the series will converge, or at least be something usable for a few terms.

By contrast non-perturbative methods can dig in where the fields are strong. In many cases the perturbative methods are too difficult to use against a continuum background so an approximation is used. Non-perturbative methods in high energy particle physics are almost all done on the lattice, and we find the non-perturnative CDT quantum gravity using their triangulations.

...

thanks for contributing this very helpful summary!

BTW selfAdj. all the published description of std. LQG I've seen (whether from proponent like Ashtekar, Rovelli or from critical outsider standpoint like Nicolai) are explictly and definitely characterize LQG as non-perturbative. Would you like some links and page refs? Not sure this matters since right now it looks like CDT has better prospects than LQG for achieving the nonper. QG goal

another BTW: as several of us doubtless know first hand, even if you have AN EXACT MODEL, say a differential equation, when it comes time to actually calculate numbers the chances are you will use numerical methods which are inherently APPROXIMATE. I certainly know that from experience! And I think several others of us do as well.

Actual numerical calculation, as selfAdj indicates, will involve approximative methods WHETHER THE MODEL IS EXACT OR whether it is a perturbation series involving successive terms that must be solved for.

===========
for the random reader: QED is a good example where the coupling constant (approx 1/137) is a small dimensionless number, its powers get small rapidly, the square, the cube, ...already tiny. So expanding in a power series works well. One problem with expanding gravity in an analogous fashion is that in 4D spacetime the coupling constant G has dimension. It is not a pure number like 1/137 is. On the other hand in 2D spacetime Newton's constant is dimensionless. A curious fact. And one that contributes to the ease of doing quantum gravity in 2D.

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

I got the idea of using the saying EXACT MODEL as the opposite of PERTURBATIVE from Smolin. He uses the word that way on page 30 of
hep-th/0408048. This is in Smolin's FAQ Section. It is actually number 1 his first "Frequently Asked Question".
See how you like the sound:

"1. How can there be a finite, well defined formulation of quantum general relativity when that theory is not normalizable in perturbation theory?
The reason is that the standard perturbative approaches make two assumptions which are not made in the exact approach followed in LQG."

 

[marcus]

selfAdjoint or anyone else who might be reading, please give me some feedback on the language, if you have any reactions!
the avowed quest or goal is "nonperturbative quantum gravity"
(a nonper theory that really works and that can be checked)

I worry that to an interested lay person "nonperturbative" just causes eyes to glaze over. trying alternative ways to say it.

I just looked at the Loops 05 conference page list of topics which include

http://loops05.aei.mpg.de/
Topics include:

Causal Sets
Dynamical Triangulations
Loop Quantum Gravity
Non-perturbative Path Integrals

I see that one of the things that unites these different research lines is they are NON-PERTURBATIVE. LQG, for instance, was at one time called Nonperturbative Quantum Gravity. Rovelli mentions this in the introduction to his book. The designation is no longer used he says because there have appeared other nonperturbative approaches.

So here is a conference involving a bunch of allied non-pert. approaches to QG. How about we call it a conference on EXACT QUANTUM GRAVITY? This is exact in the sense of not perturbative. (Number crunching is a whole other business )How about we list the topics this way:

Causal Sets
Dynamical Triangulations
Loop Quantum Gravity
Exact Path Integrals

What I am trying out is whether it would communicate better to a general audience. The scholars can keep on saying "Nonperturbative quantum theories of gravity" and "Nonperturbative gravitational path integral" and so on. I am not proposing language reforms for them! what I am thinking is how does a journalist talk about this conference?

 

[marcus]

Exact QG: the emerging theory

Now suppose this were the name of this thread. What is the message? First we have to explain that this exact does not refer to numerical calculation (almost never exact!) but it is about the model being exact: not a power series, not successive approximations. The intended model is not a perturbation series model. It is to be an exact model in that sense. That is the goal.

And then we say that something that makes the year 2005 important in the history of physics (and I do not mean 1905 I mean 2005) is this year's papers of Renate Loll. These show many things for the first time.

And mainly they show evidence that an exact (i.e. nonperturbative) QG is possible! and has signs of good behavior.

So 2005 could be the year that physics finally starts to go for an exact QG, which means that it moves into a quantum spacetime, a quantum continuum (instead of the old classical continuum)

And then the final part of the message to convey is that Lolls 5 or so papers in the past year are using one particular method (Triangulations) for doing Exact QG and that there are OTHER candidate methods that people are trying out and have been developing. And the people working on the allied lines of research all share the quest for an exact (and background independent) quantum theory of gravity and they are getting together near Berlin in October for the ("not just-")Loops 05 conference.

=======[EDIT]REPLY TO SELFADJOINT NEXT POST=====
Hi selfAdjoint, one must certainly be very cautious of calling any manmade theory "the true theory", very cautious indeed!

I didnt know that Dyson ever had the audacity, or naivety, to suggest that QED was an ultimately correct picture of nature.

I think that, in that department, the word is QUEST. I am proud that people venture on that kind of quest where they try to capture the true essence of things, what really exists. Or at least they are not satisfied with mere kludges, effective theories that produce the right numbers in some limited cases but not in others. But no one should ever entertain the illusion of having reached that goal (even the brilliant Freeman Dyson!)

 

[selfAdjoint]

Marcus, I still don['t like "exact model" as a substitute for non-perturbative. What is an exact model? The Lagrangean of QED is as exact as you like, and leads to exact Euler-Lagrange equations, but they can only be solved perturbatively. Perturbative is a physics based approximation, because the physics can't be handled. Not to be conmingled with numerical approximation. It's really the way the interaction is handled that makes the perutbative difference.

Of course you could say "true theory", as Freeman Dyson once believed QED was a true theory, before he disabused himself^*. It seems you like the idea of CDT as a "true theory" aka "what really happens". while my opinion is more standoffish.

^*The story is told in Schweber's QED and the Men Who Made It

 

[marcus]

Marcus, I still don't like "exact model" as a substitute for non-perturbative.

Nor do I much actually. BTW nonperturbativeness, as someone pointed out earlier, has a kinship to "background independent"

A recent Loll paper reminded me just now that a key thing about nonperturbative path integral is that you don't just
superpose fluctuations around a classical geometry
you superpose an entire class of geometries. this is from page 3 of
http://arxiv.org/gr-qc/0506035 [Broken]

" In a fully nonperturbative formulation... absence of a classical background structure. In the nonperturbative path integral, all possible geometries are superposed, not just those which represent fluctuations around a given classical background geometry. Semiclassical geometry emerges only..."
Among army people, I believe, there is this idea of a CADRE which means "framework" in French and if you want to build a unit you start with a core of experienced soldiers who know the drill and you add on recruits so that they can get assimilated by the core experienced people. A ship might have a skeleton crew that know the ropes and that gives something to start with.

In a perturbative path integral you start with a classical geometry and you study FLUCTUATIONS AROUND THE CLASSICAL GEOMETRY, so you don't make quantum spacetime from scratch
or make it out of whole cloth.
you have a classical model to start varying FROM, or a classical armature to hang layers of quantum fluctuation onto.

so perturbative (whatever else it means about strong/weak field coupling constants, perturbation series expanding in powers of the coupling...)
whatever else it means in the QG context, perturbative has this connotation of HAVING A CLASSICAL ANSWER TO START OUT WITH
that you perturb around, and add fuzz to and quantumly blur and add little touches or corrections to

nonperturbative has the connotation of from scratch and out of whole cloth and calling the quantum spacetime into existence with no prior classical entity there to help, as a point of departure

it bothers me that I can't think of a word for this
except of course for "nonperturbative"

 

[marcus]

bootstraping quantum spacetime into existence, with no classic point of departure

...[in this QG context] nonperturbative has the connotation of from scratch and out of whole cloth and calling the quantum spacetime into existence with no prior classical entity there to help, as a point of departure

it bothers me that I can't think of a word for this
except of course [the word itself] "nonperturbative"

to see how it sounds I am going to substitute in the word "bootstrap" as a token for "nonperturbative". I will do this with the first sentence or two of the abstract summaries of several recent Loll papers

http://arxiv.org/hep-th/0505113 [Broken]
Spectral Dimension of the Universe

We measure the spectral dimension of universes emerging from bootstrap quantum gravity, defined through state sums of causal triangulated geometries. While four-dimensional on large scales, the quantum universe appears two-dimensional at short distances...


http://arxiv.org/hep-th/0505154 [Broken]
Reconstructing the Universe

We provide detailed evidence for the claim that bootstrap quantum gravity, defined through state sums of causal triangulated geometries, possesses a large-scale limit in which the dimension of spacetime is four and the dynamics of the volume of the universe behaves semiclassically. This is a first step in reconstructing the universe from a dynamical principle at the Planck scale...

http://arxiv.org/gr-qc/0506035 [Broken]
Counting a black hole in Lorentzian product triangulations

We take a step toward a bootstrap gravitational path integral for black-hole geometries by deriving an expression for the expansion rate of null geodesic congruences in the approach of causal dynamical triangulations...

http://arxiv.org/hep-th/0507012 [Broken]
Taming the cosmological constant in 2D causal quantum gravity with topology change

As shown in previous work, there is a well-defined bootstrap gravitational path integral including an explicit sum over topologies in the setting of Causal Dynamical Triangulations in two dimensions. In this paper we derive a complete analytical solution of the quantum continuum dynamics of this model, obtained uniquely by means of a double-scaling limit. We show that the presence of infinitesimal wormholes leads to a decrease in the effective cosmological constant,...

another one: bed-rock, connotation of being hard-core, not just
perturbativing around. still thinking

 

[Chronos]

An observation, with your indulgence marcus. Bootstrapping [resampling] is a technique most statisticians, IMO, would more likely associate with perturbative theory. It is very perturbative friendly [not that it's nonperturbatively hostile]. Just a comment, not a disagreement [my inner statistician insisted I comment].

 

[marcus]

turby or not turby, that is the question

so statistics people already have made a jargon term of "bootstrap"! It means "re-sampling"?

Computerfolk, as far back as 1970 had the term "bootstrap loader" which was a short, specialized loader program of only a dozen or so machinelanguage instructions which you could toggle manually directly into the computer. the bootstrap loader would enable the computer to read paper punchtape, or punchcards, so it could then take in a longer more substantial smarter loader program, which in turn would enable it to take in the OPERATING SYSTEM

so "booting" the computer, in 1970 meant to toggle in the dozen instructions and get it to read in its official loader code, and then its operating system.

Often there was no nonvolatile memory like a disk, IIRC. so you might have to boot up just to get running.

It was like the computer raising itself by its own bootstraps because if you have a bare computer without operating system how could it ever LOAD anything? so how could you ever get the operating system into it? How do you unlock a locked box which contains the key you need to open it.

I imagine that among computerfolk the "bootstrap" term goes back much farther, I just don't happen to know how early it came into use.

I have been trying various substitute-words for "nonP", not terribly seriously but just incase something happens to ring a bell. I don't know if bootstrap has merit or not. If you would like to, give me a few synonyms for "nonperturbative". What does it mean to you? in a one-word icon if you can think of one.

 

[marcus]

another thing i think we could use, besides some good ways of talking about
Nonperturbative Quantum Gravity, and the
nonperturbative path integral (adding up all the possible geometries) approach-----besides just better ways of talking about and describing, we could use a LOLL GRAVITY PRIMER
a kind of very primitive ABC of how triangulations works and how the
computer simulations of quantum spacetime are set up.
any ideas reactions suggestions wd be real wlcme

 

[Chronos]

That is an excellent point, marcus, and illustrates how difficult it is to posit a nonperturbative theory. An analogy: Perturbative theory is a programming language and nonperturbative theory is machine language. The background state consists of on-off switches where time is the trip sequence.

 

[spinnet]

By Suresh K Maran
Hi Marcus,
Rememer me?
There is a new thread from me with title,
Critique of Lubos Motl's opinions on Loop Quantum Gravity

thanks