# The Landscape – For Real This Time

By cjohnson | August 14, 2005 1:51 am

A couple of weeks ago I used the phrase “The Landscape” in the title of a post but I was really referring to my garden, and I went on to mention there that I had deliberately chosen a misleading title for fun. Several people would not have known why this was misleading. I’d like to explain what I had in mind. This is also a continuation of the story I began in another earlier post concerning approaches to cosmology in string theory, the subject of the workshop I’m attending at the Aspen Center for Physics.

(Cautionary note: I won’t be able to include lots of details. This is meant to be a light sketch of some of the activity going on in the field, and some of the questions that have arisen, aimed at non-experts. Of course, I invite useful discussion of all levels in the comments.)

I’m going to assume that you’ll recall the discussion from the earlier post, and the sketch to the right. The curve is a very simplified illustration of a very important point. It is the potential energy curve (I’ll often just say “potential”) for one of the scalar fields in the underlying theory, and it is hoped that almost all the scalar fields produced by string theory (showing up as one of the modes of the string, like all particles do in this approach to string theory) have a potential that is a bit like that. (I’ll give you a geometrical picture of what a scalar field is, in a while, if you’re not sure what that is.) There are two key features. 1) It has a nice well in the middle. This is where the scalar will like to settle, if anywhere near the well. 2) The value of the potential at the well (where the particle will settle) is positive.

This positivity is important. Such positive contributions to the total energy of the system will break the underlying “supersymmetry” of the string theory, and give a postitive value for the cosmological constant. (This potential energy of the system is referred to as the “vacuum energy”, being the “ground state” energy associated to universe thus constructed – this is the same as what a cosmological constant is, classically anyway.) We care about both of these because we know that the world is not supersymmetric (see the earlier post for what supersymmetry is) and because it is currently believed (and this may well turn out to be wrong (!) see Mark’s recent post) that our world does have a positive cosmological constant.

I should emphasize at this point that until recently, string theory studies have been mostly focused on models which were supersymmetric, in which case they have vanishing or negative vacuum energy (cosmological constant). A huge amount of knowledge and computational technques have been developed to study such cases. The possibility (and it is still just a possibility) that our universe might have a positive cosmological constant started a big discussion within the field about whether such vacua (solutions of the theory) could be reliably constructed within string theory, because it is very hard to do. I’ve already mentioned in the previous post that various scenarios (such as those of KKLT) were eventually presented for how such vacua could be constructed. The key ingredients are well-known. They are the “branes” (extended objects) of various sorts, and I also talked about those in that post.

Let’s move on a bit. What people are doing in the field now is exploring these constructions using the string theory technology we have available. The problem is that the computational technology is right at the edge of what we can do, and it is not easy to control these vacua. This means that people are still confused as to the reliability of the solutions that have been found, but – as far as is known – the basic scenarios which generate these sorts of solutions are very plausible indeed. Allied to that fact is the realization (pointed out first in this paper and explored and developed further in this paper) that there are very many vacua spanning rather closely spaced values of the cosmological constant. So there’s a lot of choices, basically, and they look a lot like each other. So you might ask “why choose one over the other?”. We’ll come back to that in a bit.

Within the limitations of the techniques that we have for exploring the contruction of these vacua it is now understood that there are vast numbers of these vacua, and a huge amount of them may have characteristics (such as the value of the cosmological constant) comparable to our world.

So I promised in my most recent post that this would have something to do with mountains. Let’s have a closer look at the picture I took up near the Maroon Lake earlier today:

Lets’s think of height as representing potential energy, just like on our earlier sketch. Let’s think of the valley (the surface of the lake, say) as being at zero energy. Then all higher elevations are positive energy, and you see that there are several interesting features. Staying in the valley for a moment, notice that there are several positions which have the same vanishing energy and are neighbours of each other. In other words, you can move around on the surface of the lake and stay at the same height. These are the supersymmetric vacua that we understand best. The degrees of freedom to move around on the surface of the lake and visit different supersymmetric vacua without changing height (no cost in energy) are those pesky massless scalar fields (“moduli”) that I mentioned in the earlier post. Horizontal position is the value of the field – a number. We need need to break supersymmetry and fix the scalars to specific values since we know that must be so from observation of our world.

So we are somewhere at higher elevation. In fact, we want to find a solution that is like a well in our original sketch: it’s the bottom of an isolated valley somewhere up in the mountains. If you squint at the photo, you can see some of them up there in the craggy shoulders of the Maroon Bells mountains. And there are lots of hidden ones. They all have interesting properties, and some of those properties match those of our world. The new results in the field – exploring the Landscape of possibilities (Ah! Now you see where the name comes from!) suggest that there are vast numbers of these which are all very close in characteristics to our world.

This was disappointing to some poeple. This is because there was a hope that string theory might produce a single vacuum which corresponds to our world, with all properties of our world determined by this single solution. In the setup visualized in this hope, all we had to do was study hard and find this solution and thereby understand once and for all why our world is the way it is: The world would be string theoretic, as would follow from the fact that it had popped out as the unique solution to string theory. This was the old “Theory of Everything” story, which I’ve already pointed out on this blog as being frightfully naive, in my opinion (see beginning of next paragraph for why I think so). (It must be said that when Green and Schwarz pointed out the results of certain computational miracles in the early days of string theory showing that these theories -potentially containing both quantum gravity and particle physics ! – were consistent, the enthusiasm which ensued about the prospects of the theory is quite understandable. But we’re a bit more sober these days, and rightly so.)

Instead, a new movement began. The idea began to arise that maybe not everything about our universe is fundamentally computable in string theory. As I’ve said before on this blog, in view of the history of the way science has always worked (new theories take over and extend the range of applicabiltiy the old, again and again) this is not an entirely unreasonable characteristic of any physical theory. I would go as far as to say that it is perfectly fine for us to accept that this might true about string theory while still remaining extremely enthusiastic about it, given its remarkable properties.

But it did not stop there. Still hanging on to the idea that string theory is some sort of “final theory”, some people – most famously, Lenny Susskind at Stanford (who I’ve just noticed has a Wikipedia entry!) – began to combine that idea of lots of solutions (with apparently no dynamical way (physics reason) to choose just one) with the idea that our world would have to be explained by “Anthropic” reasoning (an idea which had been brought into particle physics discussions earlier by Steven Weinberg). Something along the lines of “we live in this particular solution of string theory because it has characteristics conducive to us living in this particular solution of string theory”. Many people just don’t like this approach, and say that it is no longer science. We can talk about that at length, but that’s not really the point of this post. All you need to know is that this is the origin of the Big Discussion that people will tell you is going on in string theory right now.

Sure, it’s a big discussion, but it is entirely overstated that this is the one thing occupying the minds of all string theorists, and that the fate of the entire field depends upon the outcome of this argument. (This is the impression given in publications such as the New York Times, who seldom tell you what’s going on in a field unless there’s a good controversy to present, and also on blogs such as this one.)

So why, you ask, are all these people to whom I alluded not worrying about the issue? Are they just: 1) Out of the loop? 2) Careless? 3) Begging to get their grants cut?

The answer is simple. The discussion is an interesting one to have, and it is good that there are people having it, but frankly it is far too premature to conclude much about anything about these issues. There are several things that we simply do not know about the theory, and several things over which we have little computational control. First, we do not really have a proper non-perturbative formulation of the theory. What I mean by this is that we already know that string theory is not a theory of strings. It is only describable in terms of strings when a certain parameter is rather small. This parameter (called the “string coupling” in this regime) measures how likely strings are to split into other strings or join together to make other strings, processes which can change the physics. We can compute relably when this parameter is small. In 1995 or so it was realised that when this parameter is large, we lose the nice description in terms of strings and other things happen. One of the things that can happen is that extended objects -the branes- become important, and we have not yet developed the techniques for handling all that these branes can do. And that may just be the begining of the story of the interesting physics that can happen. It is this interesting physics that has allowed us to construct these scenarios for constructing the very vacua that have begun this exciting discussion. We must not forget that we have not finished the job that we began – to understand the theory.

One key thing to note about the landscape picture is the lack of control we still have for studying the whole picture. As Steve Giddings pointed out in a seminar yesterday (here at the workshop) that he was giving on some new results in the subject, it is as though the mountains are partly shrouded in thick clouds, and so we cannot see the whole picture. (Greg Moore, in the audience, pointed out that we don’t know if we can understand how to move from one valley to another without going into the clouds either, which, to my mind, further illustrates our current limitations.) Worse than that, there is still the possibility that knowing the entire landscape using current approaches may be of limited use if there is an as yet undiscovered dynamical mechanism which favours one region of the landscape over another. What I’m saying is that by all means we should explore the Landscape and learn as much as we can, but we should remember the limitations of the techniques that we have, and so not use what we find to conclude things too hastily.

Lots of things can happen to make the Big Discussion/Argument all yesterday’s news, and most of them I’m sure I don’t know – nobody knows: that’s why it’s called “Research”. As I said, it is still possible that there is a dynamical vacuum selection mechanism out there which might reduce the huge number of apparent solutions down to a few, or even one. More conservatively, it might turn out that we learn new physics for exploring the solutions (better control of D-branes and other “R-R backgrounds”, as the terminology goes) and rule out several of them, reducing the number to something considerably less dramatic, which might help put the Anthropic philosophy to rest. This would need to be accompanied by a giving up of that need to elevate the theory to being a “Final theory”. If one just thinks of it as just a physical theory, then there is no pressure to make it explain everything.

I suspect that when we understand the theory better we will see that there are good reasons not to expect that the it need be the Final Theory. It is has anything to do with nature, it’s probably just the Next Theory, albeit a very elegant and powerful one which will change the way we think about spacetime and the entire universe. This will still be something to be extremely excited about, even though it won’t be the end of the story.

-cvj

CATEGORIZED UNDER: Science
• http://conjeturas.blogia.com/ Alejandro Rivero

nobody knows: that’s why it’s called “Research”.

I do not follow… the name “re-search” seems to imply to look again into a previous search, so it is already known Is it because of this that other languages use “in-vestig-ation” ( that translates to looking “into the small traces”, more or less)?

… albeit a very elegant and powerful one which will change the way we think about spacetime and the entire universe

Exactly: we can aim to a final theory given a way to thing about spacetime and the entire universe. Langrange/Hamilton Mechanics was the Final Theory in terms of absolute position and momenta. I would be very happy if we had a Final Theory restricted to thinking in terms of force and matter fields.

• amanda

I realise it may be asking a lot, but can you give us an idea about how a vacuum selection principle might work? I’m not asking you to propose one :-), but maybe you could give us an idea, even a totally oversimplified idea, about what such a thing might look like in principle? Has anyone made a definite proposal, even an oversimplified one?

• http://blogs.discovermagazine.com/cosmicvariance/clifford/ Clifford

Hi Amanda, good question. Well, the examples we know best are in field theory. You have a dynamical principle based on fields. You write kinetic and potential energy terms where the fields are the variables and the principle of extremiizing the action picks us out (classical) vacua. Roughly (there is more to it, but this is enough for this discussion) quantum field theory uses the same tools – say, in terms of the path integral. This is all done on the background of a given spacetime. Now this works – for the vacuum selection issue, and of course things are extremely interesting in field theory too: We’re still learning a lot about both perturbative and non-perturbative physics in that context too, but that’s maybe a different issue from the one you raised.

So you might ask why don’t we just treat string theory like a clever way of writing a field theory of an infinite number of fields (this might also resonate with Alejandro Rivero’s comment above), and so write a field theory for it? Well, this is what is called “string field theory”. This is an interesting and hard area of research. My own view is that string field theory is extremely useful for studying particular vacua of the theory, but still is incomplete as an approach, even in principle. But we don’t have a lot of examples – they are hard to construct- so I could just be plain wrong.

(It turns out that even when you can write Lagrangians in field theory, you miss interesting non-perturbative physics such as strong-weak coupling duality (sometimes to a very different field theory). We know that such dualities exist in string theory, and they even exchange the basic background spacetimes and so relying on string field theory might well be obscuring a huge amount of physics.)

Another reason to suppose that we have to do more than just field-theory-like approaches using the fields of the string is that we’ve defined those fields (either implicitly or explicitly) on a given background spacetime. But string theory contains the dynamics of spaceteime too, and so we need to find a way of expressing the dynamics of all that it describes without referring to it as a string in a particular spacetime with a particular set of modes of vibration (the fields). Otherwise we’ll never be able to see everything it has to say about how spacetimes works in conjunction with everything else. This is the “background independence” problem that Lee Smolin likes to emphasize. (I understand that there are interesting remarks about Lee’s essay by Lubos Motl here.) Lee is right, it is a problem and we’d like to get to grips with it. String theorists are not ignoring it. It’s just a hard problem, and so progress there is slow, but we’ve learned a lot in recent times, such as the holographic principle, which may be useful in that endeavour.

I don’t know if it is clear that we can’t make a lot of progress toward making contact with Nature (and real experiments) without background independent formulations. We might still be able to say some interesting things about our world. (I note that James Graber in the comment thread of the “Two Cheers…” post made an interesting remark along this line.) Actually, I think this is the spirit of what people are hoping to do when the do string phenomenology, or even when they search the Landscape for interesting models. They are using what we already know about how the world looks to do some of the searching by hand, not worrying about whether or not there is a dynamical mechanism for doing the searching that we have not already found. We can’t know in advance whether this is a useful approach or not, and so effert should be put into it, as is indeed what is happening.

Best.

-cvj

• http://www.math.columbia.edu/~woit/blog Peter Woit

Hi Clifford,

You give an excellent and very clear description of the landscape issue, and what I would characterize as the most sensible attitude one can take towards it while still believing string theory has something to do with a unified theory. I’m on vacation in Maine, so won’t take much time to comment here, but a couple remarks:

1. You claim that my blog gives the impression that the Landscape controversy “is the one thing occupying the minds of all string theorists, and that the fate of the entire field depends on the outcome of this argument.” Perhaps it gives that impression, but for the record I agree with people on both sides of this controversy: with Susskind that many string theorists are in denial about the implications of the infinite variety of conjectural vacuum states of the theory (e.g. I think it is not occupying their minds enough), with his opponents that what he is doing is pseudo-science. As for the fate of the field, I do think that if Susskind’s point of view takes over, it’s no longer a science, basically because you’ll never scientifically explain anything that way.

2. One problem with believing that a non-perturbative formulation of the theory will save the day was pointed out by Steve Shenker at the Toronto panel discussion. The best non-perturbative formulation you have is the duality with QFTs a la AdS/CFT, and if this is really a general phenomenon, there’s an infinite variety of string theories, even non-perturbatively.

• http://blogs.discovermagazine.com/cosmicvariance/clifford/ Clifford

Hi Peter,

Thanks for the comments. I hope that your time in Maine is good. (What is this word “va-ca-tion”? I must look it up some time. )

I appreciate the points (1) and (2). About (2), I would say that it is going a bit far to say that it is a problem. That would be like looking in a library for a particular book or type of book, and then if the first good book you find is from the wrong genre, you conclude that since this is the best example you have so far, the whole search is doomed.

Cheers!

-cvj

• Moshe Rozali

Good morning, I see the flame wars have not yet started… there seems to be an interesting issue in Amanda’s and Peter’s comments above. We are used to background independence and vaccuum selection in the context of field theory. We have control there over the configuration space, we know then which configuration is a stable classical solution, how states transform into each other, and which is the preferred state in a certain physical situation (though probably not in a cosmological situation).

All this brings about a desire to have similar structures in quantum gravity, including the famous background independence (by now I have worried-looking strangers in the street stopping me to ask about this). But, as Tom Banks (among others) emphasizes, it is not clear we have any right to expect this in quantum gravity, string theory or not. For example in AdS/CFT, it is pretty clear that SU(N) theories for different N are not states of the same theory. There is no physical mechanism for them to explore each other. Tom gives other interesting examples in which the intuition from field theory fails, based on semi-classical gravity only (so it is not string theory specific).

Now, suppose the conjectured vacua are actual solutions of string theory, there are many of them and they are physically disconnected in the above sense, what do you do then?

Also, very nice post Clifford, I enjoyed reading it.

best,

Moshe

• http://blogs.discovermagazine.com/cosmicvariance/clifford/ Clifford

Good food for thought, Moshe. Thanks. And thanks for the overall comment about the post.

I should stress again that I’m not pinning my hopes on a vacuum selection principle, by the way. I just don’t think we’ve explored the possibility fully.

-cvj

• http://blogs.discovermagazine.com/cosmicvariance/sean/ Sean

Moshe, when worried-looking strangers stop me in the street to ask about background independence, can I send them to you?

I think the landscape should be taken seriously, because it might be true. Some people are upset by the possibility, but that seems to be quite beside the point. String theory remains the leading quantum-gravity game in town, whether or not predicts a unique ground state. But as Clifford emphasizes, we’re a long way from understanding the complete picture, so apocalyptic predictions on either side of the landscape debate seem premature.

• Moshe Rozali

Sean,

By all means, send them to me, I guarentee I will confuse them even more…

Lots of those issues are not specific to string theory, just that string theory is now developed enough to attempt an answer. It goes without saying that one should see what the theory says without any prior prejudice. Not sure what you mean by “apocalyptic predictions”, that was not the intention of my previous comment.

best,

Moshe

• Gordon Chalmers

From the point of view of QFT, doesnt the question of
the anthropic principle
wear thin, given a constructible
background from theoretical predictions. In principle,
the exactly solvable model of gravity/standard model,
including additional KK modes can produce we hope
to measure. A finite number of obervables can be used
in a quantum action to produce the background, including extensions as the MSSM, intstantons, and the GR background, which certainly exists. The point being
that instead of the anthropic principle, why not
compute the action and find out the naturalness, rather than spending years debating it.

• Chris W.

From Sean:

I think the landscape should be taken seriously, because it might be true. Some people are upset by the possibility, but that seems to be quite beside the point.

Someone should make clear (again!) what a deeply problematic remark this is. Here’s why: If the landscape is true, then it appears to dictate a mode of explanation of features of the observed universe that badly undercuts or even demolishes the testability of the entire theoretical framework out of which the landscape came. If you can’t test the theory, ie, if you can’t say under what conditions it could be found to be false, then what scientific substance remains in the assertion that the theory is (or might be) true? At best, it seems to me, one might hope that there are some core truths mirrored in the theoretical framework that gave rise to the landscape, and these truths might someday be embodied in a theory that is truly testable. Clifford appears to be emphasizing this latter point of view.

The apparently eminently sensible statement that nature is just the way it is, and not the way we would like it to be, can be taken too far. Logically, this statement implies that the world could be constructed in such a way that its sentient inhabitants can never find testable explanations for what they observe. It seems to me inescapable that science is based on the faith that nature is not constructed in that way. Perhaps this is what Einstein meant when he said that “she is subtle, but she is not malicious”. Of course one has the right to repudiate this faith, but one should just say so, and not wrap the repudiation in a theoretical superstructure that obscures what is really being said.

• Gordon Chalmers

It actually behooves me sometimes, when the calculations are straightforward to the extent that only months are involved to achieve the demise of the ‘anthropic principle.’ All to the better.

• Fyodor

Chris W said: “If the landscape is true, then it appears to dictate….”
I think you mean, “If the landscape is true, and if the totally unjustified Susskindian presumption that the Universe is *equally likely* to select any one of its elements as a way to be born is also true, then….”

• http://www.livejournal.com/~quantoken Quantoken

Sean said:
“I think the landscape should be taken seriously, because it might be true. Some people are upset by the possibility, but that seems to be quite beside the point. String theory remains the leading quantum-gravity game in town, whether or not predicts a unique ground state.”

What do you mean “IT” “MIGHT” be true. Can you elaborate what exactly is “it”, and what do you mean “might”?

The correct wording is the landscape(s), you missed a s, a very big S, since there are 10^500 different ones of them. I do not think it is the correct English syntax to use “it” to reference to a group of objects. Maybe by using “it”, you mean one particular one, out of the 10^500, that SSTers may be able to uniquely lock down, out of all the 10^500?

There is only one kind of vacuum as far as our observation goes. For any particular one out any of the 10^500 vacuas, there is never a “might”. IT either matches our observed vacuum, or doesn’t. There is no might. There is only two possible outcomes, either all 10^500 vacuas are all wrong, or all 10^500 – 1 are wrong, except for one. And the chance that any unique math rules which keeps only one vacua and eliminate all others, also happen to give the correct vacuum, such odd is diminishingly small.

Now, I know SST already made one prediction which is wrong. SST predicted the existance of gravitons. But gravitons can NOT exist since it breaks the equivalence principle of GR!!!

Just imagine that gravity exists between ANY inertial mass, even the tinest one, even the one attributed to pure energy and not rest mass, like photons. Let’s say there is one photon of low energy and another one at the edge of the universe. These two photos STILL gravitates! According to the graviton theory they still exchange a certain number of gravitons despite the distance.

What it means is each photons needs to emit a virtually infinite number of gravitons per second, to be able to gravitate with all massed in the universe. How could energy still be conserved if there are infinite number of gravitons? And not to meantion not a single graviton has been observed.

Einstein taught us we really should not consider gravity as a conventional force. But rather, it is a pure geometry effect. The geometrization interpretation is the only correct interpretation of GR. There is no need of graviton to mediate gravity. Therefore any theory that predicts existence of graviton is wrong.

Quantoken

• http://www.livejournal.com/~quantoken Quantoken

Any theoretical physicist worth the bread and butter he earns knows full well that GR and QM are incompatible and their attempt is to reconcile the two.

So why do they took graviton for so granted, as the graviton, quantized gravity, is exactly where the incompatibility lies! Quantization of gravity field is NOT renormalizable! This is the SAME statement as saying that graviton, if exist, would have to be infinite in number. No particle can have an infinite count, so therefore if you accept the equivalence principle you have to accept that graviton does not exist, Gravity is not a force, but simply the curved geometry of spacetime.

Quantoken

• Lee Smolin

Dear Clifford,

Thanks for your piece on the landscape, which I agree is in a certain sense a very sensible view. At the same time, your stance is deeply puzzling to me. I’d like to take this opportunity to explain why, because I believe this is the core of the disagreement between those who consider themselves “string theorists” and those who like myself, remain outside the “string community”, in spite of doing some technical reserach on string theory.

You seem to reason from an unstated premise, which is that, whatever happens, string theory will turn out to be relevent for the description of nature. Even in your closing, when you contemplate different possibilities, including that string theory is just “The Next Theory” you don’t mention the possibility that string theory will just be not relevent for nature. This is also evident in the rasoning in your paramgraph: “The idea began to arise that maybe not everything about our universe is fundamentally computable in string theory… I would go as far as to say that it is perfectly fine for us to accept that this might true about string theory while still remaining extremely enthusiastic about it, given its remarkable properties.” You don’t consier the possibility that nothing will be computable in string theory because it is not the right theory.

There are two logically possible styles of reasoning about string thoery.

Method A: ASSUME 1) that there is a real non-perturbative theory behind all the approximate caclulations and 2) that it is relevent for nature. Then interpret various results, having to do with dualities, the landscape etc given these asumptions.

Method B: Look for evidence that the two assumptions of method A are true.

One evaluates results very differently, depending on whether one uses method A or method B. There is nothing wrong with using Method A from time to time, so long as the assumptions are made explicit, and the risks that are thereby taken on explicitly acknowledged. One can learn things that will turn out be true about the theory, if 1) is true, or about nature, if 2) is true. But one cannot do science only or even mostly by Method A, no matter how promsing an idea may seem. What I find disturbing in your essay, and in many conversations with string theorists is that they reason by Method A but they do not state expliclty their assumptions. This puts me often in the uncomfortable situation, when discussing with a string theorist, of having to add, “but there is one more possibility, the theory might be wrong.”

Many of us who seem fated to remain outside the “string community” are there becase we approach string theory by method B. We may, as I do, work sometimes on technical problems in string theory, motivated by our hope that evidence be uncovered that will show us whether assumptionss 1) and 2) are true or not. This leads to a different evaluations of results. For example, from the point of view of Method B work aimed to demonstrate the assumptions, such as attempts to prove conjectures like finiteness or the different dualities, is more highly valued than it seems to be by people whose work seems to grounded on the assumption that those conjectures are true.

I should emphasize that we are not being unfair here. Most of those who work on other approaches to quantum gravity and particle phsyics approach our own theories through method B. If you come to the loops05 meeting-and you are very sincerely invited-you will find that we are at least as hard on our own approaches as we are on string theory. Observing both communities, what I see is an overemphasis on self-criticism and in the non-string communities, and too much reasoninng with method A in the string community.

Nowhere is the difference stronger than in the evaluation of the landscape results. From the point of view of method A, we are just following the theory to see where it leads. Since we assume beforehand that the theory is right, this is a worthy project.

But from the point of view of method B, the failure to come up with any method to make falsiable predictions, coupled with the failure to find a fundamental, fully non-perturbative formulation of string theory, both after many years of work by many smart people, count as evidence against asssumptions 1) and 2).

I myself am drawn to the ideas of string theory, and I would be happy if they turn out to be true. But I believe an objective scientist must appraoch an untested theory by Method B rather than by Method A. The reason is that reasoning by Method A can lead to a situationi where a large group of people come to irrationally believe ini the existence of a theory they can neither construct nor test.

Another way to say this is that it is more scientific to work on problems, presented by nature, rather than theories. If we commit ourselves too strongly to theories before they are confirmed by having survivred many attempts to falsify them, we risk wasting lots of time and careers on ideas that turn out, beautiful as they are, to be false.

Another consequence of Method A seems to be a lack of interest in other directions. Someone, perhaps Moshe, said on a blog recently that if there were good results on quantum gravity people would get excited and work on them. If by “people” was meant “string theorists” this is just not the case. There have been a continuous stream of significant, non-trivial results on several background independent approaches to quantum gravity over the last 20 years and the community of people who works on such approaches is growing fast. But we see very few string theorists taking an active interest in any of these approaches. If you think I exaggerate the significance of the results, come to loops05, or look at recent papers by the speakers there. Or just talk to someone in the field.

The problem is that if you reason from Method A, you are bound to over-evaluate results in string theory, and under-evaluate results in alternative approaches, becuase you are already committed to one view being right.

Perhaps you think I am being unfair in characterizing your reasoning in terms of methd A. So let me pose a question, “What would make you give up string theory? Is there a theoretical result, an experimental discovery, or the lack of such, that woudl make you put your considerable talents in other directions?”

Lest you think this is unfair, I know the answer for myself, for each of the several theories I work on, and can happily answer the same question, if needed.

Thanks,

Lee

• http://blogs.discovermagazine.com/cosmicvariance/clifford/ Clifford

Hi Moshe,

I think Sean was not referring to anything you said, but the general chatter going around that things are in dire straits. (As mentioned in the main post).

Are any of the strangers that stop you and ask about background independence not worried-looking? Might there be any happy-looking ones? Might be a clue, you see.

Cheers,

-cvj

• http://blogs.discovermagazine.com/cosmicvariance/clifford/ Clifford

Hi Lee,

Thanks for your comments. And thanks for your valuable and insightful psychoanalysis of me and “the string community”.

As a member of the scientific community, I tend to use the customs of my people: We confront scientific ideas -when they are ready to be tested- with observations made about Nature, and when they are found wanting we discard them. I thought it was clear to everyone reading this article (and the one it is the sequel to) that this is one such scientific idea. Perhaps I was wrong.

I used the phrase “If it has anything to do with Nature…” in the last paragraph. Furthermore I thought the whole tone of the article was about research into what the correct theory of Nature is, and that this is one approach I was describing – in the second of a series of articles.

In my mentioning one approach to a problem, I did not realize that I have to stop and mention all the other approaches all the time. I just took it for granted that the intelligent reader (having seen the word “research” and other such phrases) can conclude that we don’t know the answers yet, and so we cannot know if we’re looking in the right place.

I’m so sorry if I was not clear.

Let me say it clearly for you and those people out there who you think might be confused:

“Research” is here taken to mean that we don’t yet know the answers. By examining a set of ideas to see if they contain the answers, we are allowing for the possibility that those ideas do not contain the answers.

I do apologize to anyone out there who was misled by my articles into thinking that the act of my describing a particular area of research implied that we already knew that it was the answer – before having completed the research.

I thank you, Lee.

-cvj

• http://blogs.discovermagazine.com/cosmicvariance/clifford/ Clifford

Hi again Lee,

I forgot one thing. You’re reminding us in your comments in several places that we are not as honest and hard on ourselves as those excellent people in your community. You mention “observing” our community.

Where exactly do you make these observations? The last time I saw you at the kind of workshop where the really hard work on string theory is taking place -where the kind of self-questioning and examination of the whole endeavour is put into practice- was very very many years ago in the middle to late 90’s in Santa Barbara.

Now, I’m not asking for an attendance sheet from you. Let me be the first to say that I’ve not been to all the workshops. Not even most of them. But then, neither have you. So are you sure that you should be making such pronouncements about the motivations, character, and scientific honesty of an entire community of people based on your “observations”? If so, your clarity of vision is ….. remarkable.

Cheers!

-cvj

• Moshe Rozali

Clifford,

Not sure what you mean, but I’ll be sure to check next time when someone asks me about the issue, but cannot explain what they mean exactly.

Lee,

I am glad you correctly remember what I wrote, the context was the claim by Peter Woit that string theorists are not interested in QFT. I was puzzled about this claim, since I think that exisiting research into formal aspects of string theory or of QFT are so interwoven, the two are practically indistinguishable. More generally, I think there is a long history of outside ideas having deep influence on the string community, I hope this trend continues. I will be really happy to have a chat about this when the opportunity arises.

best,

Moshe

• http://blogs.discovermagazine.com/cosmicvariance/clifford/ Clifford

Hi Moshe,

Gosh, I meant nothing deep. Just a poor attempt at a joke before my morning oatmeal!

-cvj

• http://eskesthai.blogspot.com/2005/08/explanation-on-landscape.html Plato

I’d like to thank Clifford on the approach here.

I do not want to denigrate the fine conversation being developed here, so providing link on my website from laymen perspective, to hone my understanding with a better model apprehension. Like those being shown here.

I bet it is a real slow process for some like myself.

• http://golem.ph.utexas.edu/~distler/blog/ Jacques Distler

Lee was, most recently, at Strings 2005, and he does hang out with his stringy colleagues at Perimeter.

I don’t know whether that counts for you, but it does for me.

I also don’t know what the contours of the ultimate theory of quantum gravity will look like. But I do think that it is very likely that, whatever it turns out to be, it will have classical solutions about-which it is well-approximated by a perturbative string theory. (Which is not, necessarily, to say that our world is likely to be well-approximated by a perturbative string theory.)

I could explain why I think that, but, instead, I will throw out what I see as the possible alternatives:

1) quantum gravity is never perturbative, about any of its vacua
2) it does possess perturbative vacua, but the short-distance behaviour is totally-different (non-stringy).

Discuss and enjoy …

• Moshe Rozali

Sorry Clifford, tone and any kind of subtelty are lost in this medium, I guess there may be some purpose in those smiley faces after all…

• http://blogs.discovermagazine.com/cosmicvariance/clifford/ Clifford

Jacques,

Strings meetings are not the best measures of the activity that goes on in the field. They are reports on results. There’s never much time to have open discussions about what we’re doing, where we’re going, etc. This year’s strings did (admirably and unusually) try to have an official discussion, and that is good. But panel discussions are not what I’m talking about, I’m talking about workshops and smaller meetings, where the real work gets done.

So if it “counts” for you, that’s fine. But I don’t think that going to a few meetings, (big or small) and having some colleauges that do string theory occupy the same building qualifies one to make broad comments about the scientific integrity and motivations of an entire scientific field. Not even most of the “insiders” of the string community would do that!

Cheers,

-cvj

• http://blogs.discovermagazine.com/cosmicvariance/clifford/ Clifford

Jacques,

I should say however: Thanks so much for trying to bring actual science back to the discussion, – the actual central intent of my post- rather than sociology and psychoanalysis.

By (1), are you saying that a possibility is that while gravity surely does have a perturbative regime (we’re in it most of the time when we do particle physics -so far-) you’re saying that this perturbative regime is somehow neccessarily classical? That when the theory is fully quantum, it is also neccessarily non-perturbative.

That’s interesting. But I’m not sure how this is to work. Is it really possible to consistently treat weak gravity as classical and not worry (at least in principle, if not in practice*) about the apparent internal contradicition? Or do you have some dynamial means by which the cross-over to strong coupling and switching on quantum mechanics can be done together. I can’t quite make it work, at first thought.

Oh….maybe one could formulate it as a sort of phase transition. Hmmmm….

Cheers,

-cvj

• http://blogs.discovermagazine.com/cosmicvariance/clifford/ Clifford

Hi Plato,

Thanks for the commets. And the interesting drawing and comments on your own blog.

Cheers,

-cvj

P.S. (Um, having “borrowed” my own landscape picture which I struggled so mightily to bring back from the wilderness ( ) could you please more explicitly credit your source for it on your blog? If all this string theory stuff turns out to be wrong, and the gates are shut at the other “community”, I might try for a second career as a photographer ðŸ˜‰ )

• Scott

Clifford, I don’t think you understood Lee’s point. His point was not that you didn’t acknowledge that the assumptions in A could be false but that you reasoned from the assumptions in A whithout explecitly saying so. Reasoning from B about the Landscape brings one to the conclusion that it is evidence that string theory may be a waste of time. This was his point in a nutshell, now could you please address his actual point and perhaps even his direct question to you,”What would make you give up string theory?”

• http://golem.ph.utexas.edu/~distler/blog/ Jacques Distler

By (1), are you saying that a possibility is that while gravity surely does have a perturbative regime (we’re in it most of the time when we do particle physics -so far-) you’re saying that this perturbative regime is somehow neccessarily classical? That when the theory is fully quantum, it is also neccessarily non-perturbative.

I see I have been unclear.

In the regime familiar to particle physicists, gravitational effects are suppressed by a small parameter, ε=E2/Mpl2. This is uncontroversial.

The question is: what happens when we try to probe the theory in a regime where ε is not small? Is the theory (in some instances) still weakly-coupled, or are we always in a strong-coupling (“nonperturbative”) regime?

I threw out a few possible answers to that question.

• http://golem.ph.utexas.edu/~distler/blog/ Jacques Distler

I see that <sub> and <sup> work in the Preview, but are wiped-out on posting.

This is irritating.

But, perhaps, by judiciously inserting the missing elements into my comment, you can make sense of what I wrote.

• http://blogs.discovermagazine.com/cosmicvariance/sean/ Sean

To respond briefly to Lee’s post: to most string theorists, the evidence that string theory is a consistent theory of quantum gravity is overwhelmingly stronger than the evidence in favor of any other approach leading to such a theory. We can debate whether that judgement is true or not (and it’s a worthy debate to have), but if it is true, we should hardly be surprised that most of their effort is spent elucidating properties of the theory, rather than fishing around for alternatives. Fortunately for the field, not everyone makes the same judgements, so work on alternatives does continue.

It does raise the question whether there are any results that would make people suspect that string theory was wrong. Of course it’s a hypothetical question, but I can imagine several results which would convince (or would have convinced, had they been true) most people to look elsewhere. For example, you could imagine showing that there really weren’t any non-supersymmetric vacuum states that didn’t decay in a Planck time. Or, reaching back, Green and Schwarz could have found that the anomalies didn’t cancel. Basically, one can imagine all sorts of no-go theorems for matching string theory to the real world; but our current understanding doesn’t imply any such results, so we should keep plugging.

• Aaron

Even if string theory has nothing to say about quantum gravity in the real world, results like AdS/CFT would still make it worthy of study from a physics point of view.

• http://blogs.discovermagazine.com/cosmicvariance/clifford/ Clifford

HI Scott,

Thanks!

-cvj

• http://blogs.discovermagazine.com/cosmicvariance/clifford/ Clifford

Hi Aaron,

Yes, this is a point that I (and several others) brought up on the comment stream in the “Two Cheers….” post. It is worth bringing up here again so thanks. String theory seems to be trying to tell us something profound about things that we already know are important in our descriptions of Nature: Gauge theories. So as I’ve said before, that alone is reason enough to explore it. Also as I’ve said before, not to do so can at best be described as negligent.

Cheers,

-cvj

• http://blogs.discovermagazine.com/cosmicvariance/clifford/ Clifford

Jacques – I see now! Thanks!

-cvj

• http://arunsmusings.blogspot.com Arun

Isn’t Method A saying String Theory is like QCD – lots of details to work out, but essentially correct? Perhaps Method B leads to “String Theory is like a lot of the toy QFTs – topological, exactly solvable, in not 3+1 dimensions, etc. – that give us insight into theory, but don’t apply to the real world” ?

• http://blogs.discovermagazine.com/cosmicvariance/clifford/ Clifford

I would say that a significant number of scientists (string theorists or not) are using Method C.

Method C: Use both Methods A and B in your daily research.

In other words, I don’t see why these things always have to be boiled down to stark and oversimplified choices.

And I repeat again: In attempting to explain to the non-experts what sort of work is being done in the field I am not required to remind the reader explicitly at every turn that the people involved are using a combination of methods A and B, just like a scientist in any other field does.

Cheers,

-cvj

• Chris W.

Could an administrator of this blog add a link (in the sidebar) to a help page on the use of HTML markup in comments? It would nice to know what’s available, and in particular to have help in avoiding use of markup that is unsupported although it is properly rendered at preview time. Thanks.

[Since this is off-topic, feel free to read and delete.]

• http://blogs.discovermagazine.com/cosmicvariance/clifford/ Clifford

Jacques, Chris W. We will try. Thanks for your patience.

-cvj

• http://www.math.columbia.edu/~woit/blog Peter Woit

Moshe,

I didn’t claim that “string theorists are not interested in QFT”, (or actually claim anything about what they’re interested in or not interested in). What I did say is that those not yet understood aspects of QFT that don’t have something to do with a putative string dual aren’t studied by string theorists, and that these may actually be the ones that hold the answer to how to get beyond the standard model.

Clifford and Sean,

Here’s a more specific version of Lee’s final question which I don’t think your answers to him address, and which may be related to what what he had in mind.

As long as no one can answer the question of what exactly string theory is, it seems unlikely that one can show that it is either internally inconsistent, or inconsistent with observed features of nature. If string theory is wrong (as an idea about unification), it quite possibly is wrong not because it predicts something that disagrees with experiment, but because it is essentially vacuous (as an idea about unification), consistent with virtually anything. What I’ve found shocking about recent statements by Susskind and Douglas is their apparent unwillingness to give up on string theory (as an idea about unification) even if they don’t have a plausible way to use it to ever predict anything. So, if an infinite landscape of string theory vacua really exists, so vast that it is compatible with anything that any particle experimentalist has ever measured or ever will measure, would a conclusive demonstration of this existence cause you to abandon work on string theory (as a theory ounification)?

• http://blogs.discovermagazine.com/cosmicvariance/clifford/ Clifford

Thanks Peter. I did answer that. In summary – You and Lee may have issues with the approach, beliefs and motivations of some string theorists. All I am saying is that there are several others who have different approaches, motivations and beliefs. To ascribe a set of beliefs that you don’t agree with to an entire field and then go on to condemn (in your view) all activity taking place under that banner seems to me to be a bit strong.

As regards the specific physics question: I repeat my answer to that too: I would be very happy with a stringy (or related) model -vacuum if you like- which reproduced everything we already know about Nature and then told me something specific about the results of all known experiments. Assuming those results are confirmed by the experiments, that model then becomes my framework for describing Nature until I get to a new regime where I need a new model. Forget discussions about whether there are other isolated vacua or not. I’m happy to take them one at a time! I already emphasised in my post that I don’t require the theory to give me just one vacuum. It would be nice, but it is not neccessary. You don’t require gauge theory to give you just the Standard Model of particle physics, do you? Do you question the validity of gauge theory because I can construct an SU(17) Lagrangian, whereas nature seems only to care about SU(3), SU(2), and U(1)? I hope not.

What is the problem with this? Has science not always proceeded this way? Why is there this knee-jerk reaction against treating string theory the same way as any other model of the universe?

Now if someone could prove that it is impossible to find within string theory that there is no way that it can connect to Nature….that it does not even have a chance to describe even a small and useful regime of it, then I will drop working on it -at least that application of it…there are others- immediately. But right now, most of the the field is engaged on developing the theory to the point where we can firmly honestly answer that question one way or the other – maybe formulate that proof – rather than subjecting the question to our prejudices, as seems to be more common.

Let’s try to devote our energies to understanding the theory well enough so that we can answer the question. This is what research is about. Also: This does not forbid others from looking at alternatives. If a better one comes along, I guarantee that everybody (more or less) will drop what they’re doing and work on that.

Cheers,

-cvj

• http://arunsmusings.blogspot.com Arun

CVJ, I really appreciate your patience. I’m hard pressed, however, to think of any branch of science outside of particle physics that is in the String Theory Bind – i.e., there is a huge, plausible theoretical structure with no experimental guidance. So I think Method C applies differently everywhere else in science. I’m imagining writing a little booklet for prospective physics students “How to do Science without Experiments”.

• http://blogs.discovermagazine.com/cosmicvariance/clifford/ Clifford

Arun,

Thanks for your comment, but I don’t understand. We are not working in a closed box here. The experimental guidance is a follows:

(1) Every experiment that has been done since the dawn of time.

(2) Every observation that we have made about Nature since the dawn of time.

That’s an awful lot of guidance to be getting on with. It would be nice to have more, but to say “no experimental guidance” is just….. a bit strong, shall we say.

cheers,

-cvj

• Gordon Chalmers

I tend to think that the group theory generating
the known masses and the possibly detectable

other masses will indicate naturalness of the ‘landscape’.

There seems to be an E_8 there.

• Scott

We confront scientific ideas -when they are ready to be tested- with observations made about Nature, and when they are found wanting we discard them

now that doesn’t really answer his question especially in the very plausible scenario that string theory can never be tested. You seem to be simply to imply that the question is premature, but what would make you try studying a different path absent string theory eventually becoming testable and then falsified. Ah but I see peter has already phrased this more specific question and you have answered that you would only abandon researching string theory if a better theory comes along absent experimental or theoretical(really old experimentall) falsification. So even if it becomes completely nonpredictive( beyond any doubt) you still wouldn’t try a different way.

Thanks

• Lee Smolin

Dear Clifford,

I should start by apologizing if I gave the impression that I was attacking the integrity of you or anyone else. I have enormous respect for you and in fact for most string theorists. That is why I am driven to try to understand the sources of persistent disagreement, which to me have been painful exactly because I find myself disagreeing so often with people I respect so much.

I do not think that anyone in string theory is reasoning dishonestly, or there is any issue of motive or character. But I do see that there are big differences between how different people evaluate the same set of results. For me, at least, its important to try to understand why we disagree so strongly. This is all I was trying to do.

Let’s take Sean’s statement that: “the evidence that string theory is a consistent theory of quantum gravity is overwhelmingly stronger than the evidence in favor of any other approach leading to such a theory.” To believe this you have 1) to not be among the people who are convinced that any quantum theory of gravity must be background independent and 2) believe that the true facts about string theory are given by so far unproven conjectures such as finiteness, S duality and the Maldacena conjecture. Conversely, if you believe background independence is paramount, and suspect that the failure to prove those conjectures after much work by good people might be because perhaps they are not true (at least in the strong forms needed to make string theory a quantum theory of gravity), then you disagree with Sean’s statement.

There is no reason why we should all agree about everything. But we should try as hard as we can to reach agreement where we can, that is part of being scientists. We are all in the bad situation in which each of us is surrounded by friends who easily agree with us, but faced with skeptics who are very hard to convince. This is not a good situation because we will never have definitive progress until we all agree. Everything I do is done with the hope of reaching that goal. Again, I apologize if I appeared to attack you or anyone else personally.

Thanks,

Lee

• Moshe Rozali

Peter,

As anticipated, we are back to that… so I dug up this quote

“One of the main reasons I’ve been on such an anti-string theory campaign is the attitude of string theorists that thinking about field theory is something completely understood, that only fools still think about it, real men do strings, etc…. It seems to me that this attitude has made it very hard for people to work seriously on QFT.”

I remember being puzzled by this, as I have been surrounded for many years by people doing serious work on QFT. I remember giving lots of examples of work done by string theorists on formal aspects of QFT, including but not limited to the AdS/CFT duality. All this work has the common property that it can be formulated (usually after the fact) in field theory language, but the string theory language seems to be the most efficient way of organizing and generalizing this knowledge.

What drew me into that conversation to start with is the claim that there are other interesting corners of QFT which are worth exploring, I am still extremely interested in hearing about them. Ultimately, that kind of discussion would be so much more interesting…

best,

Moshe

• http://eskesthai.blogspot.com/2005/08/explanation-on-landscape.html Plato

Um, having “borrowed” my own landscape picture which I struggled so mightily to bring back from the wilderness ( could you please more explicitly credit your source for it on your blog? If all this string theory stuff turns out to be wrong, and the gates are shut at the other “community”, I might try for a second career as a photographer )

Yes of course I always direct link these images much as I do paragraphs, as I recognize this ownership. I have corrected this particular image as Yours by accrediting it in an update.

I have many pictures like this too, going through Banff.

There is always something nice to be said about the mountain views. “Hills and Valleys” are nice too. Wayne Hu has a nice interpretation of this somewhere:)

Bloggery time seems slow to update, so it will show later.

• http://blogs.discovermagazine.com/cosmicvariance/clifford/ Clifford

Scott,

What is this!?

Ah but I see peter has already phrased this more specific question and you have answered that you would only abandon researching string theory if a better theory comes along absent experimental or theoretical(really old experimentall) falsification. So even if it becomes completely nonpredictive( beyond any doubt) you still wouldn’t try a different way.

You’re just making up stuff I did not say. Please don’t do that. It is particularly odd (adn kind of funny) to do that in the same comment thread, and within 6 comments of what I said to boot! Please re-read carefully my comment 41. My criteria for evaluating the worth of string theory are pretty standard ones for evaluating any scientific theory.

I think you and some of the other folks might have more fun arguing with someone a much more unconventional or whacky world view. My position is just good ol’ fashioned scientific practice! Sorry about that!

Cheers,

-cvj

• http://blogs.discovermagazine.com/cosmicvariance/clifford/ Clifford

Lee,

Apology accepted. Frankly, I’m reacting firmly (but politely, I hope) because I’m a bit tired of this business of people taking a few examples of a given position (taken by a minority of the field) and extrapolating that everyone who works on the subject must have the same view. It’s just not productive.

Yes, common ground upon which we can agree that progress is being made is good to seek and to find. Hopefully, the best measure on which we can agree will not be cleverly written essays from either side of the debate, but actual scientific results. There are several concrete results representing significant and unambiguous advances in understanding string theory, and its possible relation to Nature, and I’m sure there are such results in different approaches – such as yours – too. Let us celebrate that and move on with our programs, learning from each other when we can.

Best,

-cvj

• http://blogs.discovermagazine.com/cosmicvariance/sean/ Sean

I have never really understood the logical path from “landscape” to “can’t predict anything, isn’t really science.” As discussed before in the “Two Cheers” thread, I think the proper analogy is string theory:vacuum state::quantum field theory:standard model. If the landscape exists, then we have to actually go out and measure the parameters of the low-energy effective theory, rather than calculating them from first principles. Who cares? That’s exactly the situation we’ve always been in with field theory. Of course it makes the “theory of unification” promises hard to keep, but I never cared about those promises anyway, I cared about quantizing gravity.

Let’s imagine we did hard work on string theory and found two things: (1) a complete, background-independent non-perturbative formulation of the theory, and (2) a jillion vacuum states, one of which looked exactly like the Standard Model (or the MSSM, or whatever we knew about particle physics at the time). I would call the combination of those two things “a scientific theory that fit all the data”; how could anyone disagree?

Of course, if we have another complete quantum theory of gravity that also fits in with particle physics, but makes different predictions for Planck-scale phenomena, we would want to think of ways to distinguish between them experimentally. We should be so lucky.

• http://blogs.discovermagazine.com/cosmicvariance/clifford/ Clifford

Yep, I agree, Sean. See my comment 41.

It does seem that people run along that path pretty rapidly, and then start yelling. I don’t get it. The point is (in my mind, at least) that the possible* existence and validity of a Landscape of vacua has nothing to do with the Anthropic debate….that is a separate issue. See comment 41 folks.

-cvj

*possible: too early to tell. More research needed. See my original post/essay at the top of the page.

• http://blogs.discovermagazine.com/cosmicvariance/sean/ Sean

Lee– you’re completely right about the attitudes toward what is a promising theory of quantum gravity, of course. Different people disagree in good faith about which problems are fundamental and which clues are worth paying attention to, which is a good kind of disagreement to have. I would just add that one can be fully convinced that background independence is a good thing to have, without thinking that starting from background independence is the most fruitful route to pursue. Personally, I think those features you mentioned — finiteness being the most obvious — are incredibly powerful evidence that string theory is on the right track. (Even if they haven’t been proven rigorously, which things rarely are in field theory.)

• http://golem.ph.utexas.edu/~distler/blog/ Jacques Distler

Of course, if we have another complete quantum theory of gravity that also fits in with particle physics, but makes different predictions for Planck-scale phenomena, we would want to think of ways to distinguish between them experimentally. We should be so lucky.

As I explained in this post (attributing the remarks to Howard Georgi), it is a nontrivial statement that a putative “theory of quantum gravity” can predict anything about Planck-scale physics.

A further elaboration of the difficult hurdles faced by alternative “theories of quantum gravity” is sketched, but not elucidated in comments 23,29 above.

• http://www.math.columbia.edu/~woit/blog Peter Woit

Moshe,

I hope my later comments clarified that in what you quote by QFT I was referring to those aspects of QFT not accessible to study via a string dual. As an example of what I have in mind, in 2d much is known about how to understand certain QFTs in terms of representation theory of infinite dimensional groups, little is known about whether anything like this works for 3d or 4d theories. But going on about one’s favorite ideas in a comment thread to a posting on a very different topic is not a good idea….

Clifford,

In my comment I was just trying to ask you a very specific question, not to ascribe beliefs to or condemn a whole field. My reference to Susskind and Douglas was specifically to my own interpretation of certain statements of theirs, and maybe that’s even wrong.

I don’t seem to have made clear the specific question that I’m trying to get an answer to. What I’m trying to understand is whether you see the same danger in the existence of the landscape that I (and many others) see, and what your reaction to it is. What if the landscape is so vast that it contains an infinite class of vacua that agree with the standard model, and this infinite class is so vast that no falsifiable prediction about beyond standard model physics can ever be extracted from the string theory framework because of it? Do you see a danger that string theory will end up being a theory that is not falsifiable in the conventional way that physical theories have been up until now, because the landscape can describe anything? If this turns out to be the case, would you abandon string theory (as an idea about unification)?

As for the analogy with gauge theory: the standard model gauge theory is a rigid structure specified by a relatively small number of discrete choices and continuous parameters. Once this small number of things is specified, an infinite number of predictions follow and the theory is highly falsifiable: if an experiment finds a result that disagrees with the standard model, the only way to save the gauge theory framework is generally to dramatically increase the complexity of the theory, and you can’t do very much of this before you have to admit to defeat.

String theory is different in that simple compactifications don’t work, and one seems to have to use a very complicated compactification scheme even to reproduce the small number of discrete choices that partially specify the standard model. The danger of working with such complex schemes is that you may be able to get anything you want by just making things ever and ever more complex. One could imagine an alternate universe in which this was what happened when you tried to use gauge theory to explain particle physics, but if it had happened I think people would have quickly abandoned gauge theory. Will people abandon string theory if it becomes clear this is the way things are going?

• http://www.math.columbia.edu/~woit/blog Peter Woit

My last comment crossed Sean’s, but I think it explains exactly what is wrong with the

string theory is to vacuum state

as
quantum field theory is to standar model analogy.

I also don’t think the “I only care about quantum gravity, not unification with particle physics” point of view is viable. I’m less optimistic than Lee that any of us will ever see any experimental evidence relevant to quantum gravity in our lifetimes. By the current “consistent theory of quantum gravity” standards of string theory, it is looking like there’s an infinite number of them. If these theories don’t say something about particle physics, there is no way for us to tell which if any of them have anything to do with the real world.

• Moshe Rozali

Peter,

Duality a la AdS/CFT is just one of the directions in understanding QFT, others are studies of holomorphic quantities in SUSY gauge theories (which Seiberg-Witten is the most famous example), relation to matrix models and topological strings, twistors and perturbative YM, and the list goes on. I would really characterize the study of (mostly SUSY) gauge theories as one of the major themes in string theory in the last decade.

As for your example, in case you are not already aware of this, there is some talk about infinite dimensional algebras in N=4 SYM (both at weak coupling and via AdS/CFT at strong coupling). One example (apologies to all the others…) of an interesting paper on this is hep-th/0308089.

best,

Moshe

• http://blogs.discovermagazine.com/cosmicvariance/sean/ Sean

Peter’s comments reveal the crucial difference of viewpoints. If you think of string theory as primarily an attempt at unifying the forces and going beyond the Standard Model, of course you will think the landscape is a disaster. I don’t think of it that way; I’ve always thought of it as a quantum theory of gravity. As Clifford points out, there is plenty of experimental evidence that we need quantum gravity; e.g., the fact that the Earth goes around the sun.

Per Jacques’s comment, one can replace “theory of quantum gravity” with “ultraviolet completion of the Standard Model coupled to general relativity” as one wishes.

• Scott

Clifford, You answered peter’s more specific version of Lee’s question

Now if someone could prove that it is impossible to find within string theory that there is no way that it can connect to Nature….that it does not even have a chance to describe even a small and useful regime of it, then I will drop working on it -at least that application of it…there are others- immediately. But right now, most of the the field is engaged on developing the theory to the point where we can firmly honestly answer that question one way or the other – maybe formulate that proof – rather than subjecting the question to our prejudices, as seems to be more common….If a better one comes along, I guarantee that everybody (more or less) will drop what they’re doing and work on that.

So you will only start researching something else if string theory is somehow proven wrong or somebody makes up a theory you like better, but( unless you simply forgot to mention this third thing) if it is at some point shown to be completely unpredictive you don’t say you will start looking for another avenue of research. So either you failed to answer peter and my question about whether you would abandon string theory if it became apparent that it was completely vacuous or my previous comment was not out of place and was an accurate depiction of what you said. So if I am wrong please feel free to actually answer the question of what you would do if it string theory does end up to be essentially vacuous.

• http://blogs.discovermagazine.com/cosmicvariance/clifford/ Clifford

Hi Peter,

Thanks. I would still say that the criteria for determining whether to stop working on the theory or not are as stated in comment 41. I’m having trouble imagining how the scenario you outline is qualitatively differerent from the example of gauge theory and the standard model. It seems to me that it is just a matter of degree. But I allow for something odd happening, in my final paragraphs below.

First, let me state the “matter of degree” scenario. Let us say that the Landscape picture is true and you have no way of ruling out lots of solutions: there is no nonperturbative principle, say. (I’m obliged to say: This is a hypothesis for this paragraph, it may not be true!) So you find a model (stringy or otherwise) which fits all current experiments, possibly using measured data to fix some uncalculable quantities (the horror!). Or lets say you find N such models.

Then one day you do an experiment that gives some new data. If M of them don’t fit the data, you have N-M candidate models left. You refine your predictions for the next generation of experiments. If all N of them do not fit the experimental data, you throw them all out. You’ve falsified the theory. Find a new framework.

In this program, I don’t care how big N is. Even if it is infinite (in some enumerable sense) that’s ok. I can write down an infinite variety of Standard models right now, within the gauge theory framework. It does not invalidate the process of studying gauge theories and making predictions about the results of scattering experiements.

Ok, like I said, if its not a matter of degree, then I guess it is something like this. If the structure of the landscape (if it exists) is so perverse that we can’t unambiguously carry out the above scheme (I guess that’s equivalent to saying that N is uncountably infinite in some horrible sense? Whatever.), then it is indeed not a workable theory. I would then not* work on it. Big deal. Most people have no trouble saying this. It’s not like you’re getting me to admit to some horrible attrocity or something.

The point is that until we’ve done the research, we don’t know. None of us have a clue, I stress. We’ve none of us seen a theory like this before, that’s what is so exciting! Sure, we can imagine lots of horrible, unexpected, and contrived things taking place in this world, and get ourselves scared by them. Most of them don’t happen.

You mustn’t condemn a scientific endeavour on the basis of your fears about the things that might go wrong to spoil the outcome.

So let’s do the research and see what really happens.

Cheers,

-cvj

(*original version, amusingly, had the “not” missing…. but it is clear from the rest of the paragraph that I meant it to be there. Thanks Scott!)

• http://blogs.discovermagazine.com/cosmicvariance/clifford/ Clifford

Scott.

I’m puzzled again by your definitons. My mistake. In my world, to prove that a theory is unpredictive is the same as proving that it is “wrong” in some broad, but clear sense. So I did not include that possibility explicitly since I did not think of it as distinct enough to mention. My mistake. I thought that again this is standard in science. (God, I’m so old-fashioned it seems!)

Ok here goes, in short. I’m throwing down the gauntlet:

You nay-sayers out there – Here is the challenge: Work carefully and hard on string theory (please! we need the help! it’s hard!) and unambiguously prove that it has nothing to do with Nature, either because it predicts wrong answers, or because it can predict nothing. This is the best way to stop people working on it, if it disturbs you so terribly that people are working on it.

This is the way science has always proceeded.

Otherwise, please do not stand in our way because you have some idealogical reason to dislike the theory.

Best,

-cvj

• Scott

Sean,

As Clifford points out, there is plenty of experimental evidence that we need quantum gravity; e.g., the fact that the Earth goes around the sun.

Obviously the mechanics of the world are expected to be consistant, and we need to find a new theory which encompasses both QM and GR but that does not automatically mean that the way to do this is by quantizing gravity and so even though that is the most common approach tried the need for consistancy does not demand quantum gravity.

• Scott

Clifford, I don’t know if I am being dence or not, but you tell me that the completely vacuous scenario would be included in you proven wrong scenario by some strange twist of english while you tell peter.

If the structure of the landscape (if it exists) is so perverse that we can’t unambiguously carry out the above scheme (I guess that’s equivalent to saying that N is uncountably infinite in some horrible sense? Whatever.), then it is indeed not a workable theory. I would then work on it. Big deal. Most people have no trouble saying this. It’s not like you’re getting me to admit to some horrible attrocity or something.

Did you mean to type “would then not work on it” or do you somehow consider this scenario to not be the equivalent of unpredictive.

thanks in advance for the clarification

I don’t think I will accept your challenge though as I figure the other path of trying, and most likely failing, to make a better theory would be more fun.

• http://blogs.discovermagazine.com/cosmicvariance/clifford/ Clifford

Whoops! Typo!

Thanks….. (“Freudian slip!” They’ll all shout!)

-cvj

P.S. “strange twist of english”. We’re doing science here, not english. The sense is clear. I know of no “correct” theories that are inherently unpredictive. Do you? Or would you like to use Pauli’s “not even wrong” category, which inspired Peter’s blog’s name? Ok. Go ahead.

• http://www.math.columbia.edu/~woit/blog Peter Woit

Moshe,

My mistake to try to say something simple about the issue of the work done at the string theory/QFT interface. It seems to me an extremely interesting, but very complicated subject, much worth discussing, but highly off-topic here. You’re right much of this is about SUSY gauge theories, and one quick comment about them. I’ve always found the subject extremely frustrating, there’s something very right about these theories (for one thing, the mathematics is just fantastic), but there’s also something very wrong about them (the MSSM is hideous). Something very interesting is going on there, but I don’t know what. Thanks for the reference, that’s a topic I’ve never looked into, but should.

• http://www.livejournal.com/~quantoken Quantoken

According to conventional wisdom, gravitons certainly carry energy. And energy is mass, and therefore gravitons must gravitate amongst themselves, if the Equivalence Principle is still correct.

So gravitons must emit gravitons to exchange gravity force amongst themselves. Then the gravitons emitted by gravitons must also gravitate and therefore emit their own graviton, and it goes on and on, leading to a picture of infinitely many gravitons, many with incredibly small energy. But there are infinitely many gravitons nevertheless.

It then contradicts the Bekenstein Bound, if you consider the entropy represented by all the possible states all those gravitons can sit at.

To resolve the paradox, you must thus conclude that gravitons do NOT exist, and gravity is NOT a force exchanged by bosons, but merely spacetime geometry effects. And certainly, SST gets it all wrong by predicting graviton, something that does not exist.

Again, answer the damn question: “”Do gravitons gravitate amoungst themselves“?!

Quantoken

• http://www.math.columbia.edu/~woit/blog Peter Woit

Clifford,

Sorry for harassing you into stating the obvious that once one has shown a theory is unpredictive, it’s wrong (or not even wrong…) and one has to give up on it, but I think this discussion was worthwhile, it certainly helped me clarify some things for myself. And it’s helpful to see that we share fundamental criteria for evaluating science. I’m afraid that I sometimes share what I take to be Lee’s perception that for some string theorists, the possibility that the idea of string-based unification is just wrong seems to be something they won’t even admit to be a possibility.

No, I’m not going to take you up on your suggestion and devote myself to working on string theory. There are already many, many smart people doing this, and they appear to me to be doing a good job of slowly accumulating evidence that the string theory unification idea doesn’t work. I don’t think I could significantly speed that process up. I’ll stick to pointing out what other people have already found, and trying to develop what seem to me to be more promising ideas.

The main thing this clarified for me is the whole issue of falsifiability. You and Sean are right that it’s a good idea to think about the analogy between the gauge theory and string theory frameworks, although I draw different conclusions from this analogy. I guess I do think that the difference is one of degree, but that differences of degree are crucial. Whatever theoretical framework one has, one can generally find some way of making it fit the facts. If it’s a good theoretical framework it’s easy, if it’s not you have to engage in all sorts of ugly contortions. Thus, in evaluating theoretical frameworks, a sense of aesthetics is crucial, and claims like those that Susskind is making that it doesn’t matter if things are really ugly are dangerous. I’ve been thinking a lot in recent years about this kind of “aesthetic” issue, and the connection to falsifiability is something I hadn’t thought about before.

• http://blogs.discovermagazine.com/cosmicvariance/clifford/ Clifford

Peter,

I think this thread has just been fantastic! We’ve actually had a really productive discussion, and agreed that we’re all still doing science, and that several things are worth doing. We did it without all getting on our high horses, or getting abusive…..

For the non-experts, I think that our discussion may have served to clarify a lot of the mixed messages that have been put out there about what string theorists are doing, what they hope to do and also served to show why they’re just part of the whole tapestry of good science being done.

This is all just great! Let’s continue to talk!

Thanks all.

-cvj

• http://golem.ph.utexas.edu/~distler/blog/ Jacques Distler

Do gravitons gravitate amoungst themselves”?!

Yes.

Gravitational waves scatter (“gravitationally”) off each other in the classical theory, and that phenomenon had better be reproduced in the quantum theory.

Qualitatively, it’s no different than light-on-light scattering in QED. Quantitatively, light-on-light scattering is a loop effect in QED, whereas graviton-graviton scattering is a tree-level effect (which is why it persists in the classical limit).

Both are manifestations of the fact that the interacting theory is nonlinear.

• Aaron

At the risk of being a bad person and sending the thread off in another direction, I’ve failed in my attempt to not respond to the following”

Let’s take Sean’s statement that: “the evidence that string theory is a consistent theory of quantum gravity is overwhelmingly stronger than the evidence in favor of any other approach leading to such a theory.” To believe this you have 1) to not be among the people who are convinced that any quantum theory of gravity must be background independent

That’s hardly true. Background independence and string theory are not in any stark disagreement. There are those who have argued that the fundamental formulation of the theory may strongly depend on the asymptopia, but that could just as well also be an artifact of our current formulations, in particular, because asymptopia seem to be just about the only source for observables that anyone can get a handle on.

But, even beyond that, I can’t help but think that to say that any quantum theory of gravity must be background independent smacks of hubris. Nature is going to work how it’s going to work. We certainly don’t get any say in the matter.

and 2) believe that the true facts about string theory are given by so far unproven conjectures such as finiteness, S duality and the Maldacena conjecture. Conversely, if you believe background independence is paramount, and suspect that the failure to prove those conjectures after much work by good people might be because perhaps they are not true (at least in the strong forms needed to make string theory a quantum theory of gravity), then you disagree with Sean’s statement.

Since when is much of anything proven in physics? The AdS/CFT conjecture, for example, has any number of nontrivial verifications that don’t all have to do with the SUSY algebra. If some form of it isn’t true, I’d be hard pressed to understand why it works so well.

There is no reason why we should all agree about everything. But we should try as hard as we can to reach agreement where we can, that is part of being scientists.

No we shouldn’t. Science isn’t done by consensus. People have different beliefs. They should argue them. That’s good for science. If we all agreed, it’d be boring. What we shouldn’t do is assume that people with different ideas don’t understand our ideas.

• Fyodor

It’s been a great discussion. I’d like to draw attention to one aspect that hasn’t been spelled out. It’s very simple.

Before you comment on what people say, try to find out exactly what they *did* say.

This applies not just to people on this blog, but to others, particularly celebrities, outside it. For example, Mike Douglas seems to get quite a whacking in the physics blogosphere, but this seems to be based more on what legend says he is doing rather than what he actually does. Most recently, he and his co-workers claim to have found evidence that only finitely many members of the landscape can be realistic. Before blowing him away with the old “wishful thinking” routine, one should wait until they put out the paper. Then you can criticize the details if you want. Even Leonard Susskind should be allowed to explain his precise technical arguments [assuming he has any, and hasn’t fallen victim to the “anyone who disagrees with me must be engaging in wishful thinking” syndrome] for disbelieving in the existence of a vacuum selection mechanism. I would like to stress that detailed technicalia are a lot more convincing than “people have been searching for 20 years, and , like, 20 is a big number you know…”

OK, so let’s get the ball rolling: what detailed technical arguments *does* LS offer for his famous assertion that his opponents are “in denial”? What has the man *actually said*?

• http://blogs.discovermagazine.com/cosmicvariance/clifford/ Clifford

Hi Fyodor,

I gave a link to his original paper in the post. Also, I imagine that there are several talks that can be downloaded from the web. I don’t know where they are, but try the Strings 05 site, and the (K)ITP site.

When you’ve found out, please come back and tell us what you think of his arguments, in case they add a new wrinkle to the discussion.

Cheers,

-cvj

Hi Aaron,

No problem whatsoever with taking the thread in a slightly new (but clearly related) direction.

Cheers,

-cvj

• http://arunsmusings.blogspot.com Arun

I’m sorry, but to say that the earth goes around the sun is evidence for quantum gravity is a bit far-fetched. That the earth goes around the sun is not even sufficient evidence for classical General Relativity (say, at least until the 1970s).

• http://www.livejournal.com/~quantoken Quantoken

Jacques said:
“Yes. Gravitational waves scatter (“gravitationally”) off each other in the classical theory, and that phenomenon had better be reproduced in the quantum theory.

Qualitatively, itâ€™s no different than light-on-light scattering in QED. Quantitatively, light-on-light scattering is a loop effect in QED, whereas graviton-graviton scattering is a tree-level effect (which is why it persists in the classical limit).”

Good you are thinking. Of course there is difference. Huge difference. QED is renormalizable, and quantum gravity is NOT. We all know that. Another difference is those photos involved in the loop effect of QED are virtual particles that can not actually be observed. If you sum up all those virtual photons you get a ridiculous high vacuum energy density, which is 10^120 too high and that vacuum density is NOT observed by experiments.

Also it’s odd that when I talk about gravity attractions between gravitons, you call the same thing gravity-gravity-scattering. It’s not scattering as one bounce off the other at close distance. It’s gravity attraction between the two. Even two gravitons are billions of light years apart, they still attract each other gravitationally, therefore emit gravitons towards each other, and that certainly is different from scattering, which happen at close encounter. Are you sure you are not talking about the wrong concept?

The problem is unlike virtual photons, these gravitons are NOT virtual and they must be real and detectable to account for all the energy and all that in GR. The trouble is there will be infinite number of them and each is quite as detectable as the rest at least in principle. Each of the gravitons would have to carry entropy/information, since detection of any of them convoys information. Thus the Bekenstein Bound will be broken easily when you sum the entropy up.

And the solution is none of the gravitons can exist. I have been proposing a theory where the quantum entropy is a conserved quantity. It naturally leads to the existence of curved spacetime, as well as uncertainty principle, and it leads to the correct value of the Big G, as well as precise value of many of the fundamental particles.

Quantoken

• http://golem.ph.utexas.edu/~distler/blog/ Jacques Distler

Sigh!   Well, that was a wasted effort.

One hardly knows where to begin …

• http://www.livejournal.com/~quantoken Quantoken

Jacques:
Me, too!
You really think two gravitons separated by 1.4 billion light years could be “scattered” from each other? You are clearly confusing the gravity interaction between gravitons as “scattering” and you were ready to calculate cross-sections, were you. Too bad you are the one confused, not me. It was also a wasted effort on my part to try to convince you that cow’s fart/cow’s burp, whatever, really doesn’t count much in terms of green house gas.

Quantoken

• Fyodor

cvj said: “I gave a link to his original paper in the post. Also, I imagine that there are several talks that can be downloaded from the web. I don’t know where they are, but try the Strings 05 site, and the (K)ITP site.”

The original paper focuses on the existence of the landscape, not on selection mechanisms. I have searched around, but as you say the best place to look is LS’s talk at Strings 05. Unfortunately I am not able to view the recording of his talk. Anyone ? Does he spell out precisely why he does not believe in the existence of any vacuum selection principle?

• Aaron

The asked us scientist-types to not go to the public lectures to leave room for, well, the public. So, I’ve got no idea what Lenny actually said.

• http://www.math.columbia.edu/~woit/blog Peter Woit

Fyodor,

I’ve read all of Susskind and Douglas’s papers on the subject, as well as many of their presentations available on-line, and attended talks by them and asked questions afterwards, so maybe I can help you out here.

From what I’ve seen, Susskind’s argument is simply that, over 20 years of working in the area, he hasn’t seen a selection principle that works. If you want to challenge his judgement about this, you need to come up with one that does. Your favorite seems to be Tye’s recent efforts, presumably Susskind is aware of this and doesn’t think it works. You could ask him why, or consult other experts about what the problems with Tye’s program are.

As for Douglas’s conjecture that after imposing certain cut-offs the number of vacua is finite, this finiteness is irrelevant to the issue of predictivity. If there are 10 to the one-million vacua, and no structure to the landscape that picks out certain specific values of things you can observe, you can’t use it to predict anything. What’s relevant here is not finiteness, but the actual number of vacua. Finiteness is only relevant to Douglas’s program to calculate statistical distributions, and use these together with anthropic arguments and experiment input to try and make predictions. If the number of vacua is infinite, he can’t define his statistical distributions.

As far as I can tell, the problem with his program that he doesn’t have an answer for is that if he has to get finiteness by putting in cut-offs, his distributions depend on the value of the cut-off, in general ruining their usefulness for predicting anything.

• http://blogs.discovermagazine.com/cosmicvariance/clifford/ Clifford

Hi,

My understanding was (in line with what Peter said) that it is simply an assumption that there is no principle. To my mind, that assumption is paramount in what they are doing -whether they know it or not, but I’m sure they do- since if later one you were to find one, it would wipe away a lot of the conclusions one would be tempted to make about which vacua are more likely than others.

So I suspect that the Landscape practicioners are careful to distinguish between the program of simply examining vacua by hand and studying their properties (a worthy and valuable effort – see my earlier comments) and going a step further and concluding things about which ones are more likely to be chosen than others.

Cheers,

-cvj

• http://eskesthai.blogspot.com/2005/08/explanation-on-landscape.html Plato

A question.

I am thinking about Lee Smolin’s history here in terms of discrete measures ( I am developing a perspective here in relation that will be complied later) How this effected the the way Lee may have viewed the background. I don’t want to speak for Lee Smolin, but I would like to make it simple.:)

Can this difference be as simple as, “a determination between “being discrete, and implying continuity?

Where strings implying only tree features, while the approach to glast, as a “new view” supported by Doubly Special Relativity that Rovelli and Lee produced? This basis, and history is what I am compiling.

I hope Jacque your dismay with Quanto (where to begin), you will see some benefit from helping the laymen view, even to your end.

• Ian

What about Sarangi and Tye’s recent proposal about including the effects of the metric perturbative modes? These act as an environment (in the decoherence sense) and introduce a correction term which bounds the Euclidean action, thereby making the Hartle-Hawking wavefunction normalizable. One can then use this wavefunction to calculate probabilities from nothing to various places in the landscape. Needless to say, this is an interesting alternative to the anthropic principle. Furthermore shouldn’t all available alternatives be explored in detail *before* ariving at the position that anthropic reasoning is the only way out. Though of course the universe might not be so nice, and we could be forced to the anthropic perspective.

For those interested, Sarangi and Tye’s paper is here:

http://arxiv.org/abs/hep-th/0505104

• Gordon Chalmers

Again, I do have to emphasize, why not work out the backround, and then compute the observables from a QFT and/or string theory approach. It really is not difficult. Scalar field theory, for one, will be available, to arbitrary accuracy, in a few days.

• Gordon Chalmers

Would you believe it costs the same to compute a g-loop scalar amplitude than to invert an g^3 matrix inverse, approximately. I guess this is not a hot topic. It makes me wonder why gauge theory is not computed already, and also the gravitational background.

• http://eskesthai.blogspot.com/2005/06/trigger.html Plato

Unexpected High energies of Cosmic Rays Post is developing.

Experimental basis of interpretation on the “background” versus “non background?”

Seeking clarity in relation to experimental propositions of Glast 2006 and how it shall support one’s position over another? Will it?

High energy relevance had to meet each other in a way that cosmologically had somethng to do with high energy perceptions in relation to the trigger? Link on name.

The “beginning”, as first principles? Robert Laughlin saids no to “first principles”?:)

Another view thrown into the batch.

• http://eskesthai.blogspot.com/2005/06/trigger.html Plato

My question here in 81 has been answered.

I thought I would post the link that help me in that direction. It gives a nice heads up about about Loop Quantum Gravity position.

Cheers,

• Alejandro Rivero

I do not get Plato questions; we have a lot of examples where the angular momentum is discrete but the linear momentum is not, havent we? Or, for the same, the symplectic area keeps quantised while their projections (in x, p) are not.

But going back to the Landscape, a question: are we sure that even if we request for empirical agreement at low energies we do still have an infinite of vacuum solutions? IE, even if string theory happens to be not a complete predictivity, could it still be more predictive than current model builiding in HEP?

The empirical principle is weaker than the anthropical principle, but I can not see why it could not do the same work.

• http://blogs.discovermagazine.com/cosmicvariance/clifford/ Clifford

Hi Alejandro. Isn’t being predictive like being pregnant? You either are or you aren’t pregnant. One person can’t be more or less pregnant than another except in an obviously binary way. A physical theory is either predictive or it is not. Is there a sense in which one theory can be more or less predictive than another? Is the number of (implicit or explicit) undetermined parameters a useful measure, or can’t these things be compared cross-framework?

Maybe. Maybe not. What do people think?

-cvj

• Gordon Chalmers

I tend to think that even with current data we can predict. With sensitivity to numbers, accuracy in data, we can reconstruct backgrounds to physical theories, including even GR. The determination of these theories and the phenomena should be used to extrapolate also.

• Lee Smolin

Hi, if this thread is still alive, I have some comments on earlier posts:

To Aaron on background independence:

“Background independence and string theory are not in any stark disagreement.” If by this you mean that no one has proved there is no background independent formulation of string theory I agree. But this is very weak. If one exists, we should find it.

” I can’t help but think that to say that any quantum theory of gravity must be background independent smacks of hubris. Nature is going to work how it’s going to work. We certainly don’t get any say in the matter.”

Would you say the same thing about the principle of inertia? That principle is extremely well tested, but it is still possible that the quantum theory of gravity will reverse it, and return to the Aristotelian idea of a preferred state of rest. But to take the principle of inertia as something to be preserved in the next theory is hardly hubris, it is good sense to keep well tested principles unless there is a strong reason to abandon them.

But background independence has exactly the same status. It is extremely well tested at the classical level, because general relativity is background independent and its predictions are well confirmed. Were there not exactly two degrees of freedom, which is a consequence of diffeo invariance, the precise match between theory and experiment for the binary pulsar data would fail. Thus, it is only good sense to expect that this well tested principle be preserved in the next theory.

To Sean on finiteness. I’d be curious what is your understanding of the status of perturbative finiteness. Your comment seems to imply that there is very strong evidence, just short of a rigorous proof. I wish this were the case, but this is not my understanding of the situation. Perhaps you can correct me, if so I would be very grateful. My understanding is that even at a theoretical physics level of rigor all claims fall short of a complete demonstration. Either they rely on additional assumptions or do not rule out all possible sources of divergences, as in Mandelstam and Berkovitz or they go only to genus two, as in d”Hoker and Phong. Thus, this is not a typical sistuation where we theoretical phyicists have a convincing argument, awaiting only translation into a rigorous theorem. As Feynman told me in 1976 (with regard to confinement in QCD), “If lots of really smart people have tried to prove something and failed, perhaps its because it is actually not true.”

Do I personally think supersymmetric string theory is perturbatively finite? I certainly hope so, otherwise I for one have wasted a lot of time on an inconsistent theory. At the same time if after twenty years of work by really smart people, the experts on the technical issues involved have not found a complete demonstration, I don’t think we should be complacent. I would instead think we should present perturbative finiteness as a conjecture that there is some evidence for, but which remains open despite efforts to prove it. Perhaps if we emphasize that this important question is unsolved, this will motivate someone to do the hard work needed to complete the proof or find a counterexample.

• Aaron

“Background independence and string theory are not in any stark disagreement.” If by this you mean that no one has proved there is no background independent formulation of string theory I agree. But this is very weak. If one exists, we should find it.

If a nonperturbative formulation of string theory exists, we should find it. If it’s background independent, that’s great. Certainly perturbative string theory looks as if it could be the perturbation expansion of a background independent theory. But, if the nonperturbative formulation isn’t background independent, then so be it. If it (eventually) can be shown to describe the real world, that’s enough for me.

But background independence has exactly the same status. It is extremely well tested at the classical level, because general relativity is background independent and its predictions are well confirmed.

That does not follow logically. GR has been extremely well confirmed in one particular background. There haven’t been any experiments in a different background that I know about. GR’s a great theory — I’m quite fond of it. I like background independence, too. It is simply not the case, however, that it is even possible to do an experimental test of it.

Regarding your point about inertia, I’m sure I don’t have to tell you that plenty of backgrounds do have preferred frames, including our own.

Were there not exactly two degrees of freedom, which is a consequence of diffeo invariance, the precise match between theory and experiment for the binary pulsar data would fail. Thus, it is only good sense to expect that this well tested principle be preserved in the next theory.

Diff invarinance is an almost nonexistent constraint to put on a theory (as has been discussed on Usenet ad nauseum). There are strong constraints on the form that a QFT with a spin 2 particle can take, so pretty much anything will look like GR or a Brans-Dicke theory at low energy. Given that, I don’t necessarily see how the experimental confirmation of GR supports any abstract philosophical principles. What it supports is GR.

With all this said, I’d guess that an eventual nonperturbative formulation of string theory will be background independent. But, I don’t how the lack of background independence in string theory, as currently formulated, is anything other than exactly what we would expect from our current formulations. I say we work on trying to get more and better formulations rather than continually harping on whatever philosophy the theory fails to accord to. The philosophy will come out when we understand the theory, not the other way around.

• Gordon Chalmers

Are you really sure that we cannot test GR?

• Gordon Chalmers

GR really cracks me up. So does QED. Think I can get a job now?

• Gordon Chalmers

Sshhhhh…. These theories dont exist.

• Lee Smolin

Hi Aaron,

You cannot seriously mean that “It is simply not the case, however, that it is even possible to do an experimental test of it.” There is a long list of confirmed predictions of GR, some to very high precision. These strongly constrain the parameters that measure possible deviations from GR-the post Newtonian parameters.

I also can’t imagine you mean what you said: “GR has been extremely well confirmed in one particular background. There haven’t been any experiments in a different background that I know about….”

The point of GR is that the full metric is dynamical. This means that the metric emerges as a solution of the field equations. So there is no metric that is put in to define the field equations, as there is for field theories on fixed backgrounds, such as Maxwell theory or free string theory. The statement that GR is background independent is, so far as the metric is concerned, equivalant to the statement that the metric is fully dynamical. A theory of a linearized tensor field on a fixed background is unable to reproduce all the predictions that GR successfully makes.

So I just don’t know what you could mean by “GR has been extremely well confirmed in one background.” This is like saying, there is a particular Maxwell field that describes the E and B fields in the universe, which happens to be a solution to the Maxwell equations, but I don’t take that as a confirmation of the truth of the Maxwell equations.

There is one solution that describes our world but it is not a background. That one solution is incredibly complex, as the observations of lensing and the precision solar system tests all show in detail, the geometry changes dynamically, partly to reflect the distribution of matter. It has no symmetries and structure on a huge range of scales. The solution that describes our world is one of a continuous infinity of such complex generic solutions. It has no other special status. There is no plausible explanation for this than that the metric of the world is a solution to the Einstein equations, at least within a certain regime.

What I am arguing for is only that the correct quantum theory of gravity preserve the key feature of the well tested classical theory of gravity, which is that the spacetime metric is fully dynamical. This rules out theories like perturbative string theories or linearized spin two fields whose equations of motion require the prior specification of a fixed background metric.

• http://golem.ph.utexas.edu/~distler/blog/ Jacques Distler

This rules out theories like perturbative string theories or linearized spin two fields whose equations of motion require the prior specification of a fixed background metric.

That perturbation theory requires a choice of background metric (about which to perturb) is a tautology. It is equally true of perturbation theory applied to GR.

Any consistent interacting theory of a massless spin-2 field must have (the full nonlinear) diffeomorphism invariance. Perturbative string theory is diffeomorphism invariant. It also has the aforementioned (and much-maligned) split into a background metric plus perturbation.

It is hard to imagine a theory that has both full diffeomorphism invariance and a perturbative split into background metric plus perturbation, which is not, in fact, background-independent. If you can construct an example, that would be interesting.

There are other arguments for background-independence in string theory; I’m sure I don’t have to repeat them.

What we don’t have, in perturbative string theory, is manifest background-independence.

I think we can all agree that manifest background-independence would be a nice thing to have. But, in a pinch, non-manifest background-independence will do.

Personally, I’m not sure that the concept of “background independence” (as you are using the term) is even relevant to the problem of finding the fundamental formulation of string theory. “Background independence” merely requires a formulation in terms of the (full) dynamical spacetime metric. But, in string theory, there are solutions which admit multiple interpretations in terms of different spacetimes, with different spacetime metrics and different spacetime topologies.

So, when one says, “… depends only on the (full) dynamical spacetime metric,” the relevant question is, “Which metric is that?”

• Aaron

You cannot seriously mean that “It is simply not the case, however, that it is even possible to do an experimental test of it.” There is a long list of confirmed predictions of GR, some to very high precision.

“[I]t” in that sentence refers to background independence, not GR. I would have thought it was clear from context, especially as said in the previous sentence that GR had been well-confirmed.

You seem to spend the rest of your comment arguing against something I never meant. I’m using a much broader definition of background independence that you. Yours is such that I’d be astounded to meet anyone who disagrees with it. In fact, AdS/CFT seems to be pretty background independent to me given your definition.

With that in mind, I’m really rather curious exactly what evidence makes you think that string theory doesn’t have a “metric [that] is fully dynamical”. In addition to seconding everything Jacques has to say, I want to add that if you look at how the spin-2 excitation of the string exponentiates into the sigma model lagrangian on the worldsheet, it modifies the ‘background’ metric. In other words, string theory has every indication of describing a fully dynamical background metric. Certainly, the case is strong enough that I think the burden on proof is on those who argue otherwise.

Now, if you want to talk about asymptotics, you might get some argument, but that’s not what we’re talking about, I think.

• http://eskesthai.blogspot.com/2005/06/trigger.html Plato

I do not get Plato questions

It is commonly understood that General Relativity is smooth and such basis driven to a quantum perspective in string theory tree structure is also a continuum? Sorry for layman perspective. But if taken to consider bulk, then the gravitonic perception becomes such a continuum?

Well, Loop Quantum disagrees with this idea, and looking at this, the inherent difference, between loop and strings becomes apparent? Would it be of benefit to relate “Tear” of Greene to discrete function, and all would be in agreement?

Abhay Ashtekar:It turns out that partial differeiential equations of Einstein adapted to the continuum, have to be replaced by different equations, adapted to the discrete structures of Quantum Geometry

http://cgpg.gravity.psu.edu/research/articles/space&time.pdf

Brian Greene:Quantum geometry differs in substantial ways from the classical geometry underlying general relativity. For instance, topology change (the “tearing” of space) is a sensible feature of quantum geometry even though, from a classical perspective, it involves singularities. As another example, two different classical spacetime geometries can give rise to identical physical implications, again at odds with conclusions based on classical general relativity.

http://columbia-physics.net/faculty/greene.htm

Compiled info of a continued effort at comprehension in Quantum Geometry as to the basis of Loop and String/M-Theory respectively and the physics approach?

Why Loops in Glast? Strings in Colliders?

• http://blogs.discovermagazine.com/cosmicvariance/sean/ Sean

Lee, I am sure you don’t really care about my opinion on perturbartive finiteness, as I am certainly not an expert. To the order that it has been checked, the string loop expansion is finite, which is not the case for ordinary GR — i.e., it could have failed, and hasn’t yet. Obviously that’s far from a proof. My understanding is that experts don’t see any looming obstructions to finiteness, and most of them expect it to hold. I’d be happy to hear a reason to be skeptical, or of any other theories that have similar properties.

• http://eskesthai.blogspot.com/2005/06/trigger.html Plato

Here’s a description Albert Einstein gave on p. 83 of his Relativity: The Special and the General Theory:

The surface of a marble table is spread out in front of me. I can get from any one point on this table to any other point by passing continuously from one point to a “neighboring” one, and repeating this process a (large) number of times, or, in other words, by going from point to point without executing “jumps.” I am sure the reader will appreciate with sufficient clearness what I mean here by “neighbouring” and by “jumps” (if he is not too pedantic). We express this property of the surface by describing the latter as a continuum

what do we mean when we say continuum

• Lee Smolin

Dear Aaron and Jacques,

I agree that there is evidence for the existence of a background independent string theory, but this is not the same thing as to construct it. I also agree that the most convincing evidence is from the fact that a necessary condition for the conformal anomaly to vanish is that the target space satisfies the vacuum Einstein equations, to leading order and the quantum effects renormalize the metric. As to what evidence makes me think that string theory doesn’t have a metric that is fully dynamical, one is the fact that we only know the precise amplitudes for supersymmetric strings to propagate and interact in backgrounds with timelike or null killing fields, which is to say we only know that perturbative superstring theory exists, in detail, for metrics that are non-dynamical.

It may be that this limitation can be transcended. But it is good to be precise about what has been shown and what is still conjectured.

I’m heartened that we all agree that there is enough probability that a background independent formulation of string theory exists that it is worth while looking for it. So lets move on to discuss what are good strategies to look for such a theory. I know of three,

1) Construct an 11 dimensional Chern-Simons like theory. (Banados et al, Horava)

2) Construct a background independent matrix theory, and derive the existing background dependent matrix formulations of string and M theory by expanding around solutions of it (hep-th/0002009,0006137,0104050, 0212043).
3) Construct a background independent quantization of 11d supergravity (hep-th/0003285, with Yi Ling).

I’d be curious as to your view of these approaches and what other ideas you have about how to go about finding the background independent formulation of string theory.

• Gordon Chalmers

Perhaps background independence arises naturally ex-post facto. That is, solving the gravitational background to many orders in the coupling, and then testing for small perturbations or in solving the full quantum field equations. The seeming dislike of a global background independence should not be confused with a microscopic gravity formulation, and its dynamics. There should be the distinction of a Lagrangian used between global spacetimes and local microscopic ones ; this might clarify the subject of background independence.

• Gordon Chalmers

Perhaps the domain of background independence is in the laboratory of medium+ -energy nuclear physics? There is
no simple Lagrangian for this.

• Moshe Rozali

Lee,

What a bold idea, discussing physics on a blog, and on a post which has the L-word in the title…I am intrigued by the possibility of a real discussion here.

I laid out some of my confusion somewhere up there (and there’s much more…) . I am confused what degree of background independence exists in existing non-perturbative formulations of string theory, for example the AdS/CFT. In any such formulation one has fluctuating modes (which are “summed over”, at least implicitely) in the CFT, and with resepct to these modes one has full background independence.

However, one also has typically some non-fluctuating modes, which are defined by the asymptotic values of fields (or the rank of the gauge group in the CFT). Those seem to define superselection sectors, and are completely non-dynamical. This is a common feature of all holographic duals on gravity theories. Tom Banks laid out very convincing reasons (to me) why those really are superselection sectors – they cannot probe each other in any physical way.

So, taking this to be a clue, I am wondering what would a background independent string theory mean. Do you think there should be some off-shell formulation that has both AdS and flat space as two of its classical solutions?

best,

Moshe

• Aaron

As I said, I’d prefer to find nonperturbative definitions and then see if some sort of background independence flows out of them. I’m not at all convinced that there’s even going to be a metric to sum over in the end. Of course, if I had any good ideas about how to do any of this, I’d have a lot easier time getting a job.

The issues Moshe refers to, BTW, are what I was referring to in the last paragraph of my most recent comment. As I think I mentioned even earlier, I suspect that the focus on asymptotics may just be an artifact of the fact that it’s very hard to get a handle on an observable anywhere else, but I don’t really have any evidence for this.

• Gordon Chalmers

Maybe the geometry of the horizon has a lot do with any holography. This does not sound background independent.

• Gordon Chalmers

Maybe the blog owners want to take bets on what the
beta function in scalar field theories looks like to
thousands of loops. We can test twenty years of work
here. (The program isnt fully functional yet.) I
would call that background independent also, unless
the higher dimension operators in the bare theory are
included.

• Gordon Chalmers

No quantum field theorist is willing to lay his
intuition on the line?

• Lee Smolin

Hi Moshe and Aaron,

First, I agree that the focus on asymptotics is at least partly because it allows an easier class of observables to be studied. I also agree with Banks that different choices of asymptotic conditions define different classical phase spaces and hence distinct Hilbert spaces.

In classical theories, whether GR, supergravity or topological field theories this is completely clear, and can be understood in detail. The reason is that the choice of asymptotic conditions break the diffeomorphism and gauge invariance on the boundary, and this gives rise to easy versions of local physical observables defined on the boundary. Furthermore, whenever there are boundary or asymptotic conditions, boundary conditions have to be imposed and boundary terms have to be added to the action, otherwise the action is not functionally differentiable and the field equations are not defined. These boundary conditions and boundary terms then become part of the kinematical specification of the phase space. There is no phase space that unifies them. If one follows standard quantization rules they lead to distinct quantum theories.

There is also a subtle interplay between what is gauge and what are physical symmetries, whose details depend on the boundary terms and conditions. This leads to a clear separation between constraints that generate gauge invariances and observables such as energy, charge and momentum, that are defined by surface integrals at the boundary. There is more to say, but the best way to learn this stuff is to work carefully through the case of GR with different boundary terms and asymptotic conditions to see how it goes. One good, careful source is Ashtekar’s World Scientific book on the new variables. (btw the calculations are much simpler in Ashtekar variables than in ADM variables.)

The analysis leads to an understanding that the formulations with boundary or asymptotic conditions are truncations of the full theory in which the added conditions reflect the presence of external sources and currents. These can be interpreted as coming from situations we observers set up, when we wish to isolate and study a part of the universe. If we then extend this wisdom from the classical theory to our conjectured background independent quantum theory we would conclude that the basic formulation will be the one without asymptotic or boundary conditions. Once this is in closed form, it is likely that models of isolated systems can be constructed, as in the classical theory, by imposing boundary or asymptotic conditions.

Hence, I believe we only have to make one theory, and it is one without boundary or asymptotic conditions. If we can do this, we should be able to invent appropriate truncations to represent isolated systems, when needed.

Thanks,

Lee

• Gordon Chalmers

But what about ‘man-made’ systems, without gravity,that break background invariance. Assuming we can do this, wouldnt this break the notion of background invariance, if of course gravity was not involved in the first place?

• Gordon Chalmers

I dont intend to argue, as background invariance I believe you. However, I feel that there are situations in which this does not hold, in nature. And the existence of black holes should indicate this.

• Gordon Chalmers

I should probably mention quasars, pulsars, and neutron stars as examples of non-background independence.

• Moshe Rozali

Lee,

Thanks for the clear explanation of your viewpoint. I agree that a theory which is background independent in this strong sense is desirable, and we should see if we can get lucky and formulate one.

The only point which makes me hesitate is that in the non-perturbative formulations I am familiar with (AdS/CFT, various matrix models) , mainly due to their holographic nature, it seems difficult to isolate a subsystem in the manner you explained. Such a procedure presumes a degree of locality that is absent in these descriptions. Maybe there is a better, more universal and local description out there.

best,

Moshe

• Gordon Chalmers

Why is even background independence good or desirable?
That is honest.

• Aaron

I believe at some point in any discussion of observables in quantum gravity, it is imperative that someone throw something at someone else and ask if they observed it. So, regardless of holography being whatever it is, I can’t imagine that the coorect theory won’t be able to, in the end, describe isolated systems. Really, perturbative string theory can be thought of as doing precisely that.

• Gordon Chalmers

Assuming you could solve perturbative (and non-) string theory, what would background independence mean and why would it be important. Perhaps that is a more appropriate question.

• Moshe Rozali

Aaron,

When expanding around some classical background, one inherits a lot of structure from it. So when we are at almost flat space asking not too precise questions, we can get away with using local observables (which can be defined using the background). These definitions are perturbative around the given background. The issue of observables only becomes relevant when the system is strongly gravitating, so ambiguities in defining those local observables become large.

I am not sure what you mean by your statement on perturbative string theory. The only well defined objects are S-matrix elements which probe the whole spacetime.

best,

Moshe

• Gordon Chalmers

Yeah, well, Moshe, perturbative string theory well be
solved in the next year. So you can ask what background
independence means.

• Aaron

Moshe,

You could make the same statement about the S-matrix in QFT. But, of course, we still do local experiments. The S-matrix describes those experiments well enough. That’s the sense in which I meant my statement about perturbative string theory.

I’m not sure if you’re agreeing with me or disagreeing with me in your other statement. Do you think we can or cannot describe isolated systems?

• http://eskesthai.blogspot.com/2005/06/trigger.html Plato

What Lies Beneath?

Still as a layman, such general talks need better clarification? If you set the stage from planck length, then how indeed does LQG arise here?

Here’s another view.

Witten: One thing I can tell you, though, is that most string theorist’s suspect that spacetime is a emergent Phenomena in the language of condensed matter physics.

http://online.kitp.ucsb.edu/online/kitp25/witten/oh/10.html

Robert Laughlin: The true origin of these rules is the tendancy of natural systems to organize themselves according to collective principles. Many phenomena in nature are like pointillist paintings. Observing the fine details yields nothing but meaningless fact. To cor rectly understand the painting one must step back and view it as a whole. In this situation a huge number of imperfect details can add up to larger entities of great perfection. We call this effect in the physical world emergence.

http://large.stanford.edu/rbl/lectures/index.htm

• Moshe Rozali

Aaron,

Yes, difference in semantics, Lee talked about isolating subsystems for study. This imply that the isolated system is part of the universe (the whole universe is also isolated in a more trivial sense) and decouples from the rest of it. I think we are in agreement, I assumed you used Lee’s terms.

best,

Moshe

• http://eskesthai.blogspot.com/2005/06/trigger.html Plato

How would such a “landscape” bring string theory into better comprehension?

• Watcher

Background independence has been a topic in many of the comments in this thread—more than I’d like to count.

A propos of that, a paper appeared this week by Jerzy Lewandowski and others:
http://www.arxiv.org/abs/gr-qc/0508091
Background independent quantizations: the scalar field I

And sure enough Lee’s recent paper was mentioned in the first paragraph of the introduction.
—quote from Lewandowski et al introduction—
The phrase “background independent theory” means in Physics a theory defined on a bare manifold endowed with no extra structure like geometry or fixed coordinates. A prominent example is the theory of matter fields coupled to Einstein’s gravity. In the case of a background independent classical theory it is natural to assume the background independence in a corresponding quantum theory. A profound polemic devoted to that issue can be found in recent paper of Smolin [here they cite The Case for Background Independence].
—end quote—

I don’t know how complimentary Lee would consider that citation to be—I hope that in Polish a profound polemic means something nicer than the kind of polemic we have where I come from.:-)

I didn’t think that The Case for Background Independence was polemical at all! To me it sounded like friendly advice to string theorists, suggesting they work towards getting less dependent on pre-selected geometry. If the author is still in ear-shot, congratulations on a good paper. Hope it proves influential among high energy theorists!

Since Lewandowski is a leader in nonperturbative quantum gravity, and this paper is part of the important process of putting matter into the LQG picture, some readers might be interested in the abstract. Here is a brief exerpt as a sample:

“We are concerned with the issue of quantization of a scalar field in a diffeomorphism invariant manner. We apply the method used in Loop Quantum Gravity. It relies on the specific choice of scalar field variables referred to as the polymer variables. The quantization, in our formulation, amounts to introducing the ‘quantum’ polymer *-star algebra and looking for positive linear functionals, called states…”

• http://blogs.discovermagazine.com/cosmicvariance/clifford/ Clifford

Thanks. Are you the Watcher from Marvel Comics?… ðŸ˜‰ ‘Cos you could just tell us the answers then. But you won’t, right?

-cvj

• Watcher

I’ll never tell

• Aaron

“Watcher” is surely “Marcus” who has been taking posts from this thread and reposting them on physicsforums.org.

It’s annoyed me enough that I’m feeling a bit rantlike….

This continual harping on “background independence” has long since ceased being “friendly advice”. What it is is tiresome, repetitive and, generally, ignorant. The string theory perturbation expansion is exactly that, a perturbation expansion. It’s going to be a perturbation around a background metric by definition. This has absolutely no relevance as to whether or not string theory is a background independent theory or not. What it means is that we don’t have a nonperturbative definition of the theory.

In other words, background independence is a complete red herring. What we need is a nonperturbative definition of the theory. And, you know what? I don’t need Lee Smolin to tell me, over and over and over and over again, that we should find one. I’d guess the same holds for most other string theorists, too. Nobody thinks we don’t need a nonperturbative definition of the theory.

If your point is that the perturbative string is perturbative, we already know that. If your point is that the perturbative string isn’t nonperturbative, we already know that, too. So, please, tell us something new, because this is getting boring.

• http://golem.ph.utexas.edu/~distler/blog/ Jacques Distler

I should point out thatcomment 96, above, addresses the very issue of “background independence” that “Watcher” or “Marcus” or whatever his name is, is harping on.

If the objective was to actually move the ball forward, a sensible approach would be for him to address what’s already been said. Presumably, he has something else in mind.

Hence Aaron’s exasperated tone…

• Watcher

Hi Jacques,
yes I read your #96 several days ago. That is where you split the concept into
manifest background independence” and
non-manifest background independence”

I noticed however that your comment #96 didn’t seem to resolve or put an end to the discussion—indeed in comments # 97-118 the word “background” occurs over 30 times.

In my view, since people were continuing to discuss this issue and did not seem to share a common definition of the term, it was appropriate to give a link to Jerzy’s paper.

There the tone is pacific (nothing to make anyone touchy or defensive) and there is a clear definition. If you want to “move the ball” then would you perhaps agree to use what Jerzy says as a definition? I will repeat it:

quote from gr-qc/0508091 (Background Independent Quantizations: the Scalar Field)
The phrase “background independent theory” means in Physics a theory defined on a bare manifold endowed with no extra structure like geometry or fixed coordinates. A prominent example is the theory of matter fields coupled to Einstein’s gravity.

BTW I think there is possibly a logical difference between a theory being nonperturbative and being background independent, but see no point to arguing about it. If you would prefer to discuss issue in other terms and focus on the perturbative/nonperturbative distinction, I’m happy with that.

CLIFFORD! delighted by the Marvel comics connection!
Toonpedia background on the Watcher:
http://www.toonopedia.com/watcher.htm
Good principle: observe but don’t interfere

• http://golem.ph.utexas.edu/~distler/blog/ Jacques Distler

BTW I think there is possibly a logical difference between a theory being nonperturbative and being background independent, …

Maybe, since we seem to be talking past each other, you can explain what you think “background independence” would mean in the context of perturbation theory.

My contention is that perturbative string theory is as “background independent” as any perturbative theory could ever be. You seem to be disagreeing with that. If so, I’d like you to spell out the nature of your disagreement.

Moreover, your “definition” of background independence is a little glib, as Lee points out in comment 109:

… I also agree with Banks that different choices of asymptotic conditions define different classical phase spaces and hence distinct Hilbert spaces.

Finally, I will point to the (strong form of the) AdS/CFT conjecture as a nonperturbative definition of string theory in asymptotically-AdS space. This definition is manifestly background independent (in your sense, modulo the caveats about asymptotics), as it does not depend on a choice of background metric in the bulk, only on the asymptotics which — as Lee points out — enter into the definition of your Hilbert space.

(The conjecture, if I need to remind you, is that type- IIB string theory on a manifold which is topologically (and, asymptotically, also metrically) AdS^5×S^5, with “N” units of RR 5-form gauge flux on the S^5 is equivalent to an N=4 supersymmetric SU(N) gauge theory. The Hamiltonian of the full string theory is isomorphic to the Hamiltonian of the gauge theory. The observables of the string theory are in one-one correspondence with the Green’s functions of the gauge theory, and so forth.)

• Pingback: Friggin’ scientists | Cosmic Variance()

• Moshe Rozali

Jacques,

Lee cleared up my related confusion in that same comment, namely how come people still complain about the lack of background independent string theory after AdS/CFT, which is manisfestly background independent, albeit in a restricted sense (preserving asymptotic boundary conditions). There is a stronger sense of background independence, independence also of asymptotia, packaging together for example asymptotically flat space with AdS, dS etc..

One can hope to establish such mega-theory, it would certainly be convenient to have one. I personally believe there are strong indications no such thing exists, and the restricted sense (which already exists) is all we should hope for. Again there don’t seem to be any physical processes connecting these different backgrounds, so the question is not really to come up with a clever enough formalism.

best,

Moshe

• http://golem.ph.utexas.edu/~distler/blog/ Jacques Distler

Moshe,

Yes, I’m well-aware of this, “stronger” sense of background-independence, and I share your doubts about it. But that wasn’t the statement of background-independence that “Watcher” was claiming here.

I don’t know about “Watcher,” but I suspect that Lee’s complaint about AdS/CFT has less to do with “strong version” of background-independence and more to do with the purported “uniqueness” theorem that he frequently cites to the effect that any background-independent (in the weak sense, used by “Watcher”) quantization of gravity+… involves a Hilbert space of LQG-type.

Here we see a background-independent quantum string theory, whose Hilbert space is a nice, separable, Hilbert space of a supersymmetric gauge theory.

• Aaron

What Lee said was, “The statement that GR is background independent is, so far as the metric is concerned, equivalant to the statement that the metric is fully dynamical.”. I took his later statement to mean that he agreed that the dependency on asymptotics is probably not a sign of a fundamental background dependence — a position I agree with, but others differ on.

I don’t know of a scintilla of evidence that the metric is not fully dynamical in string theory. There is plenty of evidence, as I know I don’t have to tell you, that it is fully dynamical. So, if background independence really is summarized by Lee’s statement above, and not some statement about a weaker background structure, be it topological or asymptotic or whatever, then I really don’t understand what the issue is. It seems like continual harping that string theory doesn’t have a general nonperturbative definition dressed up in metaphysical language. There is no great philosophical disagreement here. Everyone agrees that string theory should be defined beyond the perturbation expansion.

So, forgive me if, after hearing it for the fifty zillionth time, this “friendly advice” feels more like a bit of ill-informed condescension.

• Watcher

responding to Jacques comment #109.

Jacques, I see an opportunity for us to be in full agreement on something. This would please me because I don’t care much for arguing. For definiteness I am thinking here of Jerzy’s simple definition of background independence—the very common notion that one starts with a bare manifold and avoids using a prior-chosen metric.

Again for definiteness, let’s say we are talking about perturbative methods which REQUIRE prior choice of background metric, which I think is the case when you refer to perturbation. I don’t see how any theory relying on such could be background independent, it seems an obvious impossibility!

So it seems to me you are asking me to describe an impossibility when you say:

[Maybe… you can explain what you think “background independence” would mean in the context of perturbation theory.]

I hope we are in agreement about this. Perturbation commonly relies on a background metric and so, in that context, background independence (in the sense defined) is not a possibility.
————————————-

However because the ideas are logically distinct, we should be able to go outside the usual context and find a case where they don’t coincide. I should mention this paper, for example, where there is a perturbation theory which does not require a background metric

http://www.arxiv.org/abs/hep-th/0501191
Quantum gravity in terms of topological observables ,
Laurent Freidel, Artem Starodubtsev

“We recast the action principle of four dimensional General Relativity so that it becomes amenable for perturbation theory which doesn’t break general covariance. The coupling constant becomes dimensionless (G_{Newton} Lambda) and extremely small 10^{-120}. We give an expression for the generating functional of perturbation theory. We show that the partition function of quantum General Relativity can be expressed as an expectation value of a certain topologically invariant observable. This sets up a framework in which quantum gravity can be studied perturbatively using the techniques of topological quantum field theory.”

I mention this not to recommend the paper to you (perhaps you have already discussed it on your blog, or perhaps not—-I should not presume in any case) but simply to illustrate that the two ideas are logically separate

In the context that probably most of us are familiar with, perturbative implies reliance on a background metric.

However outside that familiar context, perturbative does not always imply reliance on a background metric.

The Freidel/Starodubtsev paper is just one example—there must be plenty of others—to illustrate that one cannot simply equate the two ideas.

—————————
Oh, I am afraid I disagree with you in your next paragraph!
You say:
[My contention is that perturbative string theory is as “background independent” as any perturbative theory could ever be. ]

I believe that perturbative string theory employs a background metric, so it simply is not background independent. The definition is quite clear.
General Relativity doesnt use a prior-chosen metric and in quantizing GR an effort is made to retain this feature.

The Freidel/Starodubtsev example shows that a perturbative theory need not use a background metric—-the perturbation series can be defined in another fashion.

So I think one cannot say. as you do, that “perturbative string theory is as background independent as any perturbative theory could ever be.”

I hate to disagree, but unless I am mistaken I am forced to here.

You say “glib”.
But I actually don’t find the simple definition of background independence that I quoted from the Lewandowski paper glib. It is a very commonly used one, clear, easy to apply, and understood by a lot of people. So I think I will stick with that. Thanks for offering alternatives though.

• Watcher

sorry, I mean Jacques #129

• http://golem.ph.utexas.edu/~distler/blog/ Jacques Distler

Again for definiteness, let’s say we are talking about perturbative methods which REQUIRE prior choice of background metric, which I think is the case when you refer to perturbation. I don’t see how any theory relying on such could be background independent, it seems an obvious impossibility!

The sense in which perturbation theory is background independent (though not manifestly background independent) has been explained ad nauseum. Rather than cause Aaron to tear his hair out in frustration by attempting to explain it yet again, I will leave it to you, as a homework exercise, to reread the discussions on this subject and figure out the difference between background independence and manifest background independence.

General Relativity doesn’t use a prior-chosen metric and in quantizing GR an effort is made to retain this feature.

General Relativity, when treated in (DeWitt-Feynman) perturbation theory, is still General Relativity.

It seems to me that you are fixated on the notion that perturbation theory is the root of all evil. If that’s the extent of your argument, then there really is nothing to discuss.

The Freidel/Starodubtsev example shows that a perturbative theory need not use a background metricÃ¢â‚¬”-the perturbation series can be defined in another fashion.

Having had a long discussion of their paper over at my blog, I can say with considerable confidence that you are confused about what they have done (or not done).

But I actually don’t find the simple definition of background independence that I quoted from the Lewandowski paper glib.

I don’t care how congenial you find it. I explained why it’s inadequate.

And I also explained why, once you fix up that definition, AdS/CFT is a stellar example of a background independent formulation of a quantum theory of gravity.

• Watcher

Hi Jacques, thanks for your reply. You posed me a question in your comment #129, which I tried to respond to in my #134. Now I would like to ask in turn, and get your reply to something that interests me.

I was drawn to this discussion for two reasons, primarily. One was that it contained a lot of reaction (implied or explicit) to Smolin’s recent

http://citebase.eprints.org/cgi-bin/citations?id=oai:arXiv.org:hep-th/0507235

and I was impressed by the general reception shown here, particularly of the main thesis.
—quote introduction hep-th/0507235—
Now here is my thesis, which it is the task of this essay to support:

The reason that we do not have a fundamental formulation of string theory, from which it might be possible to resolve the challenge posed by the landscape, is that it has been so far developed as a background dependent theory. This is despite there being compelling arguments that a fundamental theory must be background independent. Whether string theory turns out to describe nature or not, there are now few alternatives but to approach the problems of unification and quantum gravity from a background independent perspective.
—end quote—

What I would like from you, if you would please oblige me by supplying it, is a concise summary of your reaction to this thesis in Smolin’s terms.

One point to stress here is that obviously terms can be defined different way and if you use someone else’s definition then you can say that string theory IS background independent. But in the sense I am used to it is NOT. So I would like for you, for a moment, to adopt Smolin’s construction (according to which string theory has not so far been given a background independent development) and to consider the main thesis of Smolin’s paper. It comes in three parts:

A. “The reason that we do not have a fundamental formulation of string theory, from which it might be possible to resolve the challenge posed by the landscape, is that it has been so far developed as a background dependent theory.”

B. “…there are now few alternatives but to approach the problems of unification and quantum gravity from a background independent perspective.”

C. (implicit) This is possible. In particular a background independent, in Smolin’s sense, formulation of string theory can fruitfully be pursued.

As evidence that a background independent formulation (in the sense of Smolin) is POSSIBLE I will cite just one recent paper as an example. I am sure you know this one, but someone reading along with us might not:

http://citebase.eprints.org/cgi-bin/citations?id=oai:arXiv.org:hep-th/0503140
A quantization of topological M theory
Lee Smolin

the relevance here, obviously, is that since the paper is by the same person the terminology can be assumed consistent. An approach to formulating string theory is offered which is background independent in the same sense as in the other paper. Here is the first paragraph or so, of that paper:

—-quote intro hep-th/0503140—
Approaches to quantum gravity have so far fallen into two broad classes, according to whether they are background independent or background dependent. So far most work on string and M theory has been based background dependent methods and ideas. But it has long been acknowledged that this was a temporary expedient and that the ultimate principles of string theory must be formulated in background independent terms. Meanwhile, a great deal of progress has been made on background independent approaches, including loop quantum gravity[1, 2] , causal sets[3] and lorentzian dynamical triangulations[4].

The results of these, especially loop quantum gravity (LQG), have inspired a few attempts to approach string or M theory from a background independent perspective[5, 6]. These make use of one of the most powerful observations of LQG, which is that theories of gravity are closely related to topological field theories[2]. The precise relation is that gravitational theories are constrained topological field theories…
—end quote—

I look forward to your responses to these three parts of the thesis, Jacques.
C. Do you think a b.i. (in Smolin’s sense) formulation is possible?
B. Do you agree with Smolin that it would be a good thing for string theorists to work on at present?
and finally, perhaps the most difficult and ambiguous part,
A. Do you see any difficulties in the present situation in string theory that might be attributable to there having been insufficient attention given to a b.i. (in Smolin’s sense) development?

thanks in advance for your response. I am hoping for something that boils it down in one concise statement and a single uniform choice of terms.

• http://golem.ph.utexas.edu/~distler/blog/ Jacques Distler

One point to stress here is that obviously terms can be defined different way and if you use someone else’s definition then you can say that string theory IS background independent. But in the sense I am used to it is NOT.

Are you interested in my reaction to Smolin’s thesis, or yours?

If you’re interested in Smolin’s, then Lee, above, acknowledged the importance of asymptotia in defining the Hilbert space of a “background independent” theory.

We have a manifestly background independent (in the sense relevant to Smolin’s thesis) formulation of String Theory in asymptotically AdS space.

With N=1 (as opposed to N=4) supersymmetry, there is, indeed, a landscape of such vacua, and no, having a background-independent formulation has not “resolve[d] the challenge posed by th[at] landscape.”

(Perhaps I simply don’t know what “challenge” he’s talking about. )

We don’t have a nonperturbative formulation for asymptotically flat spaces. Hence, in that case, we don’t have manifest background independence, as we did in asymptotically AdS. And the situation for (metastable) “de Sitter” vacua is far, far murkier still. We don’t even know what the “right” observables are in that case.

I, like everyone else, would love to have a nonperturbative, manifestly background independent formulation of String Theory. Getting there is certainly going to require new ideas.

I’m very much open to new ideas.

But the flip-side of that is that I believe it is stupid to go around telling people, “You should follow approach X.” If we knew what approach was going to succeed, we wouldn’t be wasting time debating the matter, we’d just do it.

The history of String Theory, indeed the history of Physics, shows that the crucial new insights often come from unexpected directions. A “frontal assault” on a hard problem is not usually the most likely path to success.

• Aaron

I’m just going to sob in the corner over here for a while.

Don’t mind me.

• Moshe Rozali

Watcher,

I was given a very good explanation on what Lee means by BI above, but you seem to have a slightly different definition. If some problems in string theory are attributed to lack of BI, and we should all get our acts together etc., maybe first we should agree on a definition of this term which is not yet acheived in string theory…

With your definition (which is weaker than Lee’s) AdS/CFT is already as background independent theory as one can get (also string PT, but let’s not get hung upon that). Beyond just a definition, what are exactly the **physical** problems caused by lack of BI? is there any example of known theory which goes bizerk when quantized around a background? having principles is nice, but maybe trying to solve concrete problems is a better research programme.

best,

Moshe

• http://www-stud.uni-essen.de/~sb0264 Urs Schreiber

Hi Marcus,

as has been pointed out several times in this thread (as well as elsewhere), everybody agrees on Lee Smolin’s statement which you cite if you replace

‘background dependent’ –> ‘perturbative’

and

‘background independent’ –> ‘nonperturbative’

everywhere. This is also what Lee Smolin himself must mean by these terms (I am sure) because, as has been pointed out, too, saying that a perturbative expansion needs a background to perturb about is an empty statement.

So, let me just take that piece of text which you quoted above and make these substitutions and you’ll see that everybody, really everybody, quite easily agrees (and has always agreed on):

The reason that we do not have a fundamental formulation of string theory, from which it might be possible to resolve the challenge posed by the landscape, is that it has been so far developed as a perturbative theory. This is despite there being compelling arguments that a fundamental theory must be nonperturbative. Whether string theory turns out to describe nature or not, there are now few alternatives but to approach the problems of unification and quantum gravity from a nonperturbative perspective.

That’s all. We all agree!

The only difference between different ‘camps’ in quantum gravity is the strategy by which the nonperturbative definition of quantum gravity is being searched for.

In string theory the tendency has been to study the perturbative expansion, which has the slight advantage of being actually known, and try to extract from it hints for what its unknown nonperturbative completetion could look like. Such hints include the insight that 11D SUGRA describes the nonperturbative description in a certain regime, and that Matrix Mechanics and dual CFT theories have something to do with the nonperturbative formulation. It is noteworthy that none of these insights are likely to have been obtained without guidance from rather elaborate investigation into perturbative dynamics.

In other approaches people have instead tried to write down a complete nonperturbative definition of quantum gravity in one step. A disdain for ‘backgrounds’ (but in sense 2!)) has lead them to proposals which are not easily shown to be related to classical gravity, currently.

In the end, what counts is having the nonperturbative definition of quantum gravity, no matter which way you arrive there.

• Watcher

Since you cited it, pllease read Smolin comment #109 again Jacques

—quote Smolin #109—
…The analysis leads to an understanding that the formulations with boundary or asymptotic conditions are truncations of the full theory in which the added conditions reflect the presence of external sources and currents. These can be interpreted as coming from situations we observers set up, when we wish to isolate and study a part of the universe. If we then extend this wisdom from the classical theory to our conjectured background independent quantum theory we would conclude that the basic formulation will be the one without asymptotic or boundary conditions. Once this is in closed form, it is likely that models of isolated systems can be constructed, as in the classical theory, by imposing boundary or asymptotic conditions.

Hence, I believe we only have to make one theory, and it is one without boundary or asymptotic conditions. If we can do this, we should be able to invent appropriate truncations to represent isolated systems, when needed.
—end quote—

I think it is pretty clear that Smolin is saying here that a theory depending on conditions specified on a boundary or asymptotic conditions is NOT background independent. In fact he repeats this, and elaborates on it, in hep-th/0507235.

I think you will grant (especially on rereading #109) that string theory has NOT been given a b.i. development in Smolin’s sense, which is, in fact, what he says in the paper we are discussing, and comment #109 does not change this.

I look forward with great interest to your explicit reaction to Smolin’s thesis, which I divided up for our convenience into points A, B, C. Please proceed.

• http://blogs.discovermagazine.com/cosmicvariance/clifford/ Clifford

Quoting Smolin, the Watcher said:

The reason that we do not have a fundamental formulation of string theory, from which it might be possible to resolve the challenge posed by the landscape, is that it has been so far developed as a background dependent theory.

My question (rhetorical-I don’t expect an answer) is this: How can anyone know this in advance?!

It is an interesting statement (depending upon how vaguely one defined background independence), but it is not a profound one. Please don’t get confused about this. A particular researcher might suspect this statement to be true, based on their particular experience and training, that this is the missing ingredient, but they cannot know. They would be giving the impression of knowing, which is not the same thing. If Lee Smolin knew that this was true in any precise and useful sense, then he would know what the formulation is, wouldn’t he?

Now, by following whatever route, when/if we do find the “correct” formulation, (I am obliged to say: assuming that there is one…) and perhaps find that it is indeed background independent (most likely in a sense that none of us had thought of) then that will be a cause for celebration. But it is not very useful to elevate looking for background independence as some sort of principle or manifesto. Lee reminds us from time to time that this is a thing that it would be nice to have, and I think that is a good reminder to have (thanks Lee!), but let’s not get our knickers in a twist here.

Another example -closely related- is the issue of holography. Yes, it would be nice to find a way of incorporating holography (which seems to be an important feature of quantum gravity) into some final form of the theory. It’s a cool thing, sure, we’ll take it. But all the examples of holography that we have are rather different realizations – very situation dependent. This is because holography is not very prescriptive, only descriptive. The “principle” -such as it is- only tells you how the degrees of freedom of the theory “ought” to be rearranged. It tells you nothing about how the theory might acheive this. Not a useful thing to use as a guiding principle -at least not until we have better variables adapted to this, if ever.

Much better (i.m.h.o., which you are free to ignore and carry on with your own program; I don’t write manifestos) will be to find better ways -using clues we already have- of describing the physics without explicit reference to any particular spacetime. The biggest clue (or collection of clues: T-duality, S-duality, Mirror symmetry, open-closed dualities, etc) that we have from string theory to these issues is that spacetime is not fundamental. We need to keep chipping away at learning how strings and branes deal with this. Then, no doubt, we’ll find background independence and holography and all sorts of other wonders after the fact.

Cheers,

-cvj

• Moshe Rozali

I think to make the discussion useful, maybe we should fix our definitions. There is a “weak” sense of BI, which is the most commonly used: no explicit reference to background metric, the metric being fully dynamical, etc. etc. (comments 123,128 above) If we were living a decade ago we would have fascinating discussions on whether or not string perturbation theory acheives that. Here and now we have a few examples where string theory is as BI as one can wish for. If one still wants to complain about the issue, one needs to use a stronger definition of BI, a definition that is not already satisfied by string theory…watcher seems to have done this transition only recently (comment 142)

Lee gives a good definition of a stronger sense of BI above (comment 109), my feeling is that it is too strong to be realistic, but of course as everyone points out we cannot know in advance. I just wanted to comment that the issue has been reduced to exactly what flavor of BI is desirable and acheivable. Everyone is entitled to have their own gut feeling about this.

(and for the record, perturbative/NP is a different issue in my mind)

best,

Moshe

• Watcher

Clifford, enjoying this avatar very much thanks to you for the reminder of Marvel cosmics from several decades back! Being the Watcher is a kick!

I like Urs experiment with substituting “nonperturbative” for “b.i.”

Not sure it is logically quite the same (see my earlier comment about this) but it is still a good statement to consider. Is Urs right that everyone here would subscribe to his rewording of what Smolin said?

Here is Urs rewording:

The reason that we do not have a fundamental formulation of string theory, from which it might be possible to resolve the challenge posed by the landscape, is that it has been so far developed as a perturbative theory. This is despite there being compelling arguments that a fundamental theory must be nonperturbative. Whether string theory turns out to describe nature or not, there are now few alternatives but to approach the problems of unification and quantum gravity from a nonperturbative perspective.

For my part I agree wholeheartedly. As to whether it is the same thing Smolin had in mind, it would be better to ask Smolin. He may have had some significant reason for saying what he did (b.i. instead of nonpert.) They tend to coincide in familiar circumstances but are, I believe, logically distinct.

Anyway Urs says everybody would agree to what he just said. If true that would be very nice—just having agreement is worth a lot whether or not it is the same as the original statement.

I will try to respond to some other comments, time permitting.

• http://golem.ph.utexas.edu/~distler/blog/ Jacques Distler

The analysis leads to an understanding that the formulations with boundary or asymptotic conditions are truncations of the full theory in which the added conditions reflect the presence of external sources and currents. These can be interpreted as coming from situations we observers set up, when we wish to isolate and study a part of the universe. If we then extend this wisdom from the classical theory to our conjectured background independent quantum theory we would conclude that the basic formulation will be the one without asymptotic or boundary conditions.

That, stronger version of “background independence” is pure wishful thinking. In LQG (or anyone else’s conjectured formalism), the asymptotics enter into the definition of the Hilbert space. They also radically affect the nature of the quantum observables. Smolin is conjecturing the existence of an “ur” quantum theory in which (say) both AdS and flat-space asymptotics can be treated as different “truncations” of that “ur” theory.

In a metaphysical sense, I agree with Lee that “String Theory in asymptotically AdS space” and “String Theory in asymptotically flat space” are different quantizations of ‘the same’ theory. But that is not a terribly useful observation.

I personally doubt very much whether any such “ur” theory exists as a quantum mechanical theory (of strings, LQG, or anything else).

I’ve already addressed the weaker form of background independence. As far as I can tell, it sheds no light on “the landscape.” As to the stronger form, since it unlikely to exist, I’m not sure how to assess what light it might shed, were it to exist.

• Aaron

I’ll say it one more time for Marcus: In every formulation of string theory, it looks exactly as one would expect a background independent theory to look in that situation.

Now I’ll go back to sobbing.

• http://www-stud.uni-essen.de/~sb0264 Urs Schreiber

and for the record, perturbative/NP is a different issue in my mind)

With perturbative/NP we all agree on what is meant. ‘Background’ on the other hand is used all the time in at least two different ways:

1) a non-dynamical parameter

2) a classical solution one perturbs about .

manifest BI/non-manifest BI in sense 2) is pretty much the same as perturbative/NP, by definition.

Asymptotic boundary conditions, on the other hand, are an example of background in sense 1).

• Watcher

Moshe, when I joined the discussion I offered a definition of b.i. which I think can be naturally construed to mean that the manifold has no boundary or, if it does, there are no prior conditions imposed there. Please correct me if I am mistaken. Here is comment #123 where I quoted Lewandowski:

http://www.arxiv.org/abs/gr-qc/0508091
Background independent quantizations: the scalar field I

Ã¢â‚¬”quote from Lewandowski et al introductionÃ¢â‚¬”
The phrase “background independent theory” means in Physics a theory defined on a bare manifold endowed with no extra structure like geometry or fixed coordinates. A prominent example is the theory of matter fields coupled to Einstein’s gravity. In the case of a background independent classical theory it is natural to assume the background independence in a corresponding quantum theory.
—end quote—

Boundary conditions are, I believe, extra structure. My impression is that in the AdS/CFT picture they are chosen rather arbitrarily and do not correspond to my idea of background independence or, I think, to Lewandowski et al. Indeed Lewandowski cites Smolin “The Case for…” in the next sentence, and in that paper the whole issue of boundary conditions is discussed and treated on a similar footing as a prior-chosen metric.

I am often careless and neglect to mention this. At any event, I believe the definition I offered is not limited to what you call the “weak” b.i. where all that is required is a fully dynamic metric.

Moshe you say:

“I think to make the discussion useful, maybe we should fix our definitions.”

I heartily agree! I also am very glad you mentioned this:

“Lee gives a good definition of a stronger sense of BI above (comment 109)…”

Indeed I think the stronger sense he suggests there COINCIDES with what he means by background independence in his recent paper, in the statement of the main thesis.

I think that implicitly we are all discussing this paper hep-th/0507235 “The case for B.I.” And in particular we are discussing the main thesis. So what B.I. means in the main thesis is the B.I. we should be talking about.

Your post sounds as if you possibly would disagree with part C—you might say that achieving a B.I. string formulation may be impossible, but I don’t want to presume. In any case it seems like a step in the right direction to getting clear reactions to Smolin thesis points A, B, C. Appreciate this and hope you will state your views on all three points.

for completeness, I’ll recall them:
A. “The reason that we do not have a fundamental formulation of string theory, from which it might be possible to resolve the challenge posed by the landscape, is that it has been so far developed as a background dependent theory.”

B. “…there are now few alternatives but to approach the problems of unification and quantum gravity from a background independent perspective.”

C. (implicit) This is possible. In particular a background independent, in Smolin’s sense, formulation of string theory can fruitfully be pursued.

• http://blogs.discovermagazine.com/cosmicvariance/clifford/ Clifford

Did I use a white-on-white font-on-background combination for my comment 143?!

Apparently so… But it does not show up as such on my browser….. ðŸ˜€

-cvj

• Aaron

Point A is either tautalogical or vacuous. Take your pick.
Point B is false.
Point C has been adequately answered any number of times, including Clifford’s white on white comment and Jacques’s comments 138 and 146.

• Watcher

Aaron great! I was worrying about you over there weeping in the corner
I will try to assemble yours and Cliffords #143.
Clifford I am still having a little trouble boiling your answer down to the kind of short answer form I am hoping for, but i will try.

Here then is kind of a first draft of responses to Smolin’s main thesis in “The Case for…” remember this is B.I. in Smolin’s sense used in that paper which I guess is akin to Jacques “manifest” and to Moshe’s “strong” but for me the simplest is what Jerzy Lewandowski said or else Smolin #109 or direct from Smolin’s paper.

A. “The reason that we do not have a fundamental formulation of string theory, from which it might be possible to resolve the challenge posed by the landscape, is that it has been so far developed as a background dependent theory.”

Aaron: “tautalogical”
Watcher: Aaron, I believe actually it is not a tautology. I believe he is GUESSING that if people had put more effort into developing a B.I. theory they might be working on something besides a plethora of differently compactified manifolds. The landscape quandary might not have arisen, or they might have found a way out. As a general rule THE LESS EXTRA STRUCTURE YOU ASSUME THE MORE PREDICTIVE THE MODEL, and that might apply. Smolin can correct me if I am wrong but I think point A is an educated guess and not a tautology.

B. “…there are now few alternatives but to approach the problems of unification and quantum gravity from a background independent perspective.”

Aaron: “false”
Watcher: OK I am happy. What drives me is I am really curious to see how folks respond to Smolin thesis. Simply dismissing point B as false is fine. Maybe someone else will give some reasons.

C. (implicit) This is possible. In particular a background independent, in Smolin’s sense, formulation of string theory can fruitfully be pursued.

Watcher: Thank you Aaron, what is the answer then? Does it agree with what Moshe says?

Moshe: “Lee gives a good definition of a stronger sense of BI above (comment 109), my feeling is that it is too strong to be realistic,”
Watcher: Thank you kindly Moshe, it is Lee’s definition we are talking about because it is his thesis. So you feel that string theory is incapable of a B.I. formulation, in Smolin’s sense?

You could be right. Why does Smolin think differently? He offered several links to papers he thought might be pointing in the right direction. Has anyone looked at them? Moshe, I accept your response gratefully and hope i have it right. But it worries me.

This is just a first draft. I will try to work in Clifford’s reaction too. Hope other reactions to A, B, C will be forthcoming.

• Aaron

I don’t have any idea what background independent means at this point.

My feeling is that string theory does not give any indication of needing an a priori backgound, and that every formulation yet developed reflects this fact. Others think that a dependence upon asymptopia is unavoidable.

Furthermore, I feel that the best way to answer this question is to understand string theory nonperturbatively, and then we’ll see. If, after all this, the nonperturbative formulation requires a background structure (global hyperbolicity, say), then so be it. Trying to shoehorn a given theory into some philosophical pigeonhole strikes me as counterproductive. Thus, I think the idea that string theory isn’t understood because people haven’t been thinking “background independent”ly or whatever is silly. String theory isn’t understood because it isn’t understood. String theory hasn’t been developed in a background dependent manner; it’s been developed based on the things we understand and can do. Maldacena didn’t invent his conjecture because he wanted to come up with something where the bulk metric is a dynamical variable. Rather, the conjecture resulted from the development of what we already know and some background structure disappeared. It’s all very easy to go out proclaiming that we should think about this philosophy or that program; it’s a lot harder to actualy follow that program.

So, we have this cavilling that string theory isn’t background independent when there is every indication that it is, and we have these pronouncements from on high about how string theorists should be pursuing background independence. Well, the only way to get a handle on these questions is to understand the theory nonperturbatively because perturbation theory necessitates a background, and it’s hardly an original idea that we should try to understand the theory nonperturbatively. Really, it’s completely banal. Furthermore, it so happens this is a hard problem. It’s not that nobody thinks about this; it’s that it is not easy. So, stripped of demonstrably irrelevant metaphysical baggage, what this sideline griping amouts to is a complaint that people haven’t solved a really hard problem yet. Sorry. We’ll try to be smarter.

Point B is false simply by looking at hep-th. Plenty of people have learned and are continuing to learn all sorts of things without worrying about metaphysics like background independence. In fact, I can’t think of a single interesting result in string theory that has followed from thinking about ‘background independence.’

For C, read the posts to which I referred. Jacques, for example, explained some of the reasons why people suspect that you’re always going to see a dependence on asymptotic structure. Your questions have already been answered over and over again. You just don’t seem to be reading them.

• Moshe Rozali

Watcher,

The discussion so far has the flavor of biblical scholarship, sadly. I spent way too much time in my youth hearing about what great scholars said in the far past, what did they really mean when they said it, what did the later interpretation of their words really mean etc etc., maybe that’s the reason I became a physicist….

So, to answer quickly, and get on with other things…I think the weak form of BI is already established in string theory. I have no indication that any stronger form is needed to solve any physical problem. There are indications that any stronger form would be either vacous or wrong (based on semiclassical GR alone with no reference to string theory). See for example hep-th 0306074 where Tom banks lays out a case I find very convincing. The gist is that there is no physical sense in which asymptotically different backgrounds can communicate with each other, so packaging them together will be again, either vacous or wrong.

Of course, the most sensible thing is what Clifford said, nobody knows.

best,

Moshe

• Watcher

Moshe, just read your post and like the tone. To me, it sounds like a wrap. As time permits i will try to incorporate what you said, together with Clifford’s and what Aaron points to Jacques saying, or some subset of the above, and make a second draft that summarizes the reactions (to points ABC) expressed here.

Moshe you should know better than regret your young Saturdays wasted by arguments about the Law, IMHO, as long as you got to argue yourself. its good for the brain.

thanks to everybody, I’m glad to have some concise explicit responses direct right at the message of that Smolin paper. BTW still think it is an important paper and worth this kind of exercise.

still hoping other people will say what they think on those three points—speaking for themselves: not saying what they think Jacques said or whatever—because these are matters of opinion (as so many of the most important issues are) and I’d expect quite a range. wouldn’t expect there to be one right answer.

cheers all

• Aaron

People have answered these issues, repeatedly, in their own words. If you can’t see that, I don’t know what else to say to you.

And the most important issues are not matters of opinion.

• Moshe Rozali

Watcher,

Didn’t say anything about Saturdays, in Israel there is that ancient tradition- when your party loses the election your kids get to memeorize the winner’s ideology…looks like the US is trying out that system…

But that is for another day.

best,

Moshe

• Fyodor

Just so that Aaron won’t feel so bad: I have found it really quite useful to follow this discussion. So it isn’t *completely* futile. The comment that really crystallized things for me was JD’s
“That, stronger version of “background independence” is pure wishful thinking. In LQG (or anyone else’s conjectured formalism), the asymptotics enter into the definition of the Hilbert space. They also radically affect the nature of the quantum observables. Smolin is conjecturing the existence of an “ur” quantum theory in which (say) both AdS and flat-space asymptotics can be treated as different “truncations” of that “ur” theory.”

Just one comment here: “wishful thinking” is a favourite phrase of a couple of people with whom I think JD would rather not be associated……

• http://golem.ph.utexas.edu/~distler/blog/ Jacques Distler

Just one comment here: “wishful thinking” is a favourite phrase of a couple of people with whom I think JD would rather not be associated…

But, unlike those people, I don’t mean it as an insult.

It’s sometimes useful to speculate about things that don’t exist. There is, currently, no proposed formalism for quantum gravity that is background independent in this strong sense (but several that are background independent in various weaker senses). So, while it may be an interesting thing to speculate about, it is not, as Marcus would wish, a useful criterion for deciding between different approaches.

• Watcher

Jacques: There is, currently, no proposed formalism for quantum gravity that is background independent in this strong sense

that is interesting jacques, please tell me about the path integral approach known as causal dynamical triangulations (CDT). how does it fail to be background independent in the sense of Smolin?

• http://golem.ph.utexas.edu/~distler/blog/ Jacques Distler

For the reason that has been repeated umpteen times already: the Hilbert space (or, since we’re doing path integrals, the quantum observables) depend on the asymptotics. Most investigations into CDT (though I’m far from familiar with all the literature) seem to focus on the case of compact spatial topology which is, itself, a choice of “asymptotia”.

Have my responses been unclear? I seem to be repeating myself endlessly, and yet you keep asking questions I’ve already answered.

• Aaron

CDT also requires global hyperbolicity which is a form of background dependence.

• Watcher

Jacques, just to let you know where I stand as regards your post about CDT and “asymptotia”, let me recall that my question is why you think CDT fails to be background independent in the sense in which Smolin uses the term in his paper “The Case for…”. Expect everyone knows this, but repeat it just to be sure: I am not asking whether it fails to be background independent according to someone else’s definition.

Anyone is welcome make up a definition of B.I. which CDT fails to satisfy, but that would seem not to correspond to what is in the paper. It is the thesis of that paper we’ve been discussing and that necessitates keeping to the defininitions of terms.

In “The Case for…” Smolin uses CDT as an illustration of what he means by a background independent approach to quantum gravity.

Either Smolin is using the term inconsistently, or else, your construction of Smolin comment #109 notwithstanding, CDT satisfies Smolin’s idea of a background independent approach to quantum gravity. Perhaps we can most easily clear this up simply by asking Smolin.

For my part, I see a considerable difference between the AdS/CFT dependence on a differentiable manifold with boundary, and conditions stipulated on that boundary, in string theory on the one hand, and, in CDT on the other hand, chosing a compact spatial manifold without boundary like S3 for computational purposes.

You say:
“Most investigations into CDT (though I’m far from familiar with all the literature) seem to focus on the case of compact spatial topology…”

That is right—typically compact without boundary, and for computational convenience the CDT spacetime is often arranged to be compact without boundary. My impression that the CDT computer modeling focuses on the compact case because the computer can only keep track of a finite number of simplices, though I’ve not seen any indication that the theory is limited to a compact case.

Topology change has been studied in lower dimensionality—so far not in 4D as far as I know, although that seems to be the program.

You have mentioned Smolin comment #109—that has mostly to do with boundary conditions or asymptotic boundary conditions: “asymptotia”. The concluding paragraph of #109 is as follows.

Hence, I believe we only have to make one theory, and it is one without boundary or asymptotic conditions. If we can do this, we should be able to invent appropriate truncations to represent isolated systems, when needed.

that, I think, is a pretty good characterization of Smolin’s idea of background independence and (practical choice of a compact boundaryless spatial topology like S3 for purposes of calculation notwithstanding) also a pretty good description of how CDT looks

• http://golem.ph.utexas.edu/~distler/blog/ Jacques Distler

Either Smolin is using the term inconsistently, or else, your construction of Smolin comment #109 notwithstanding, CDT satisfies Smolin’s idea of a background independent approach to quantum gravity.

This is getting tiresome. Stop quoting scripture and start thinking.

If CDT is background independent in the strong sense of comment 109, then either there is a (bijective) map between the observables of CDT with spatial topology S^3 and those of CDT with spatial topology R^3 or, perhaps, they can both be viewed as a “truncation” of some “ur” theory.

If you claim that there is such a bijective map, then tell me what it is or point me to a paper which describes it.

I am fairly confident that you cannot, because no such map exists.

(Moreover, I’m quite confident that, in the R^3 case, one needs to specify some asymptotic behaviour of the triangulations to even have a prayer of making the CDT path integral well-defined. This, in turn, will affect what the observables are.)

If, on the other hand, these are different truncations of some “ur” theory, then tell me what that theory is, or better yet, write a paper about it.

Otherwise, these are just different theories (in the same way that, in a canonical, rather than path-integral approach, theories with different Hilbert spaces are different theories).

If the observables in the S^3 and R^3 case are different. If, in fact, the observables in the R^3 case depend on the asymptotics of the triangulations, then I don’t see in what sense you can claim that this theory obeys the strong form of BI outlined in comment 109.

Word games and scriptural citations (“Smolin says so”) are not a satisfactory response. If you have an argument, make one.

• Aaron

As far as I can tell, CDT, as described in 0505154, requires a choice of a topological background. In other words, the Hilbert space explicitly only describes spatial slices of a fixed topology. This is analogous to the situation in AdS/CFT where the Hilbert space only describes spacetimes that are asymptotically AdS.

In addition, as best I can tell, the background in CDT must split into time x space. That is a further bit of background structure. Do you now want to define background independence to mean independence of background structure other than time/space splitting? Or background independence other than the topology of the spatial slices?

How exactly does one decide which background structures “count” and which don’t?

• Watcher

Aaron your #165 has two good observations which (in Jacques words IIRC “move the discussion along”)

1. “analogous”—-Indeed in 0505154 the spatial slices are topologically S^3. they may be too rough to have a differentiable structure, but they have a topology. You wish to compare the spatial slices having a certain topology (but not necessarily any differentiable manifold structure at all) in the the CDT case with spacetimes being assymptotically AdS in the other case. Why not? though some may see a difference in degree as regards the strength of the assumption.

My comment would be that 3 papers by Loll and Westra (the third has another author and appeared this year) are concerned with allowing a limited topology change but only so far in the 2D case.

I suppose the program is to remove the restriction that all spatial slices have the same topology, but we do not know if this effort will succeed.

2. “split”—-You correctly observe that the topological space used as a basis in CDT is foliated. The path integral sums over all possible piecewise flat manifolds which triangulate this with a certain size simplex, which then is allowed to go to zero.

I wouldn’t expect the limiting spacetime defined by the observables to be piecewise flat (!) nor to have a differentiable manifold structure, to the extent that one can talk about such a thing through the observables. But I imagine it to be foliated.

This foliation represents the idea of causality (in other circumstances the absence of timelike loops). You then ask a very reasonable question about the RANKING of background structure.

In “The Case for…” background independence is treated as a MATTER OF DEGREE, as if one were to paraphrase George Orwell and say

All theories of quantum gravity are to some extent background dependent, but some are more background independent than others.

“How exactly does one decide which background structures ‘count’ and which don’t?”

I would rephrase that as how does one rank the seriousness of assumptions about the underlying continuum.

We are talking about Smolin’s view as described in his paper and he clearly has some ranking in mind, because he uses CDT as an example of a theory that is comparatively more background independent than string theories.

I think his main message to other string theorists in that paper is “try to make the theory more background independent and see what happens” but that is my free paraphrase of his main thesis and it’s not really fair to try to interpret.

I think you have a fair question which you ought to put to Smolin—-about how to RANK the importance of assumed structure.

• Aaron

I really don’t care about how many angels can fit on a background structure or what Smolin thinks about it. As I’ve said many times, I think we should understand the theory nonperturbatively and see what comes of it.

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