This week I’m in Seattle, among other things attending a Summer Institute in Algebraic Geometry sponsored by the AMS. This is the latest in a series of large summer conferences on algebraic geometry that have taken place about every ten years. The last one was in Santa Cruz in the mid 90s, the one before that at Bowdoin in the mid 80s. This one is being billed as “the largest algebraic geometry meeting in the history of the world”, with about 320 mathematicians here this week, and a total of around 600 planning on showing up for at least part of the three weeks during which the conference is taking place. The full schedule of talks is on-line, and copies of speaker’s notes and transparencies should soon be appearing there.

The main topic of the first week is billed as “interactions with physics”, but there’s actually not a whole lot of that going on here. The organizers originally hoped that Robbert Dijkgraaf would be lecturing this week, but that didn’t work out. Kentaro Hori of Toronto is giving a series of three talks on mirror symmetry, and some of his lecture notes are already on-line. Rahul Pandharipande started off the conference with the first in what looks like it will be a very interesting series of lectures on Gromov-Witten invariants. This has now become a huge subfield of algebraic geometry, with many ramifications, some of which have been inspired by physics, and there continues to be active interaction between math and physics around this subject. Many of the talks in the afternoon parallel sessions are also related to this topic.

An unrelated note: Lee Smolin has a rather philosophical, but interesting, new preprint out entitled The case for background independence

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You mentioned the new Smolin article (“what’s wrong with string theory, how to fix it with background independence, and other thoughts” heh heh) http://arxiv.org/hep-th/0507235

He is probably right and I hope string theorists read and heed this article.

The new article also provides a survey of the various nonperturbative/backgroundindependent approaches to QG (Loop, CDT, causal sets…) same ones represented at Loops 05 conference. It has thumbnail accounts of various approaches and lots of references. So for some purposes it is a de facto review article (as well as proposing a cure for string theory).

Here, for instance, is the description of CDT, beginning on page 21,

—quote from Smolin’s paper—

5.3 Causal dynamical triangulation models

These are models for quantum gravity, based on a very simple construction[26]-[32]. A quantum spacetime is represented by a combinatorial structure, which consists of a large number N of d dimensional simplexes (triangles for two dimensions, tetrahedra for three etc.) glued together to form a discrete approximation to a spacetime. Each such discrete spacetime is given an amplitude, which is gotten from a discrete approximation to the action for general relativity. Additional conditions are imposed, which guarantee that the resulting structure is the triangulation of some smooth

manifold (otherwise there is a severe inverse problem.) For simplicity the edge lengths are taken to be all equal to a fundamental scale, which is considered a short distance cutoff. One defines the quantum theory of gravity by a discrete form of the sum over histories path integral, in which one sums over all such discrete quantum spacetimes, each weighed by its amplitude.

—end quote—

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Does anyone have a subscription to “contemporary physics”?

http://www.ingentaconnect.com/content/tandf/tcph

I understand that the May-June issue will have a commissioned article on CDT. or some issue soon to appear.

I very much doubt that Smolin’s article will convince anyone. He talks about the Newton/Leibniz [etc] dispute over absolutism/relationalism, decides that relationalism is obviously right, and then argues that what ails string theory is that it isn’t relational. He even mentions Mach’s principle and worries that general relativity doesn’t really make acceleration relative [doh!]. Something tells me that string theorists [and others] are unlikely to slap their heads and say, “Goddamnit! Of course! The way to understand a small cosmological constant is to make everything relational!!” I’m afraid that the response is more likely to be, “So string theory is absolutist and not relationalist? Who gives the proverbial rat’s ass?”

Four equations in forty-six pages. Positively Banksian.

I rather think it’s quite an act of hubris, myself, to say that the “correct quantum theory of gravity must be” anything. It’ll be what it is, and we’ll have to live with it. Regardless, I think generally most people think that the end theory will be background independent, so I really don’t why various loopy types spend so much time arguing for it.

And just on a quick glance, it is certainly

notalways true (p. 24) that nonsupersymmetric theories contain a tachyon. The SO(16)xSO(16) heterotic (discussed briefly in Polchinski, I believe) is an example. As for his discussion for the meaning of the ‘height’ function in the landscape, it’s not energy; it’s just a term in the action. The stationary points are the vacua and they’re stable if they have no massless scalars of tachyons.For the string theorist

“Not only, we are told, is string theory a consistent theory of quantum gravity, but it\uffffs a theory of everything, gives us wonderful new insights into gauge theories, and possesses a mathematical beauty that is so compelling that the theory simply must be correct.”

Sean.It is many times more bold than Smolin claims, but i don’t see your efforts for critizing bold string theory claims.

Your

“I think generally most people think that the end theory will be background independent”

>was no true into string theory comunity only 12 years ago. Then string theorists claimed that one would not take GR “too seriously”. In fact, a theorist (James Graber) still maintain (three days ago in Cosmic variance) the old posture that one would ignore background independence and formulate causality in a flat metric.

He claims that we would ignore experimental data on favor of string theory!

But string theory community has a special facility for forgeting the history of the field.

Fortunately, history shows how wrong string theorists always were.

A waste of time!

Aaron Bergman said:

“…As for his discussion for the meaning of the ‘height’ function in the landscape, it’s not energy…”

Which is precisely the point Smolin was trying to make.

The sad thing is that string theorists feel so embattled and animosity between camps runs so deep that enjoyable, non-technical, profound papers by very smart people are only given a “

quick glance”.The propaganda and indoctrination (from all camps) is amazing. It seems the more a camp is criticized, the more ardent in their beliefs they become. Often to the point that they’re unable to even consider the merits of another camps arguments.

…If you’re not a fellow string theorist everything you say is

a prioriwrong…If you don’t believe in Causal sets I don’t want to hear anything you have to say…But then again, I shouldn’t be surprised. This same phenomena is present everywhere else (see modern day american policital discourse).

As I’ve said before, the same rules that govern the schmucks in the street, govern us in the Ivory towers.

Wow. I’m sorta surprised that an alg. geometry conference billed as one of the largest gatherings doesn’t have some of the leading men in that area as part of their speakers–ie. Drinfeld, Beilinson, Deligne, etc etc.

The sad thing is that string theorists feel so embattled and animosity between camps runs so deep that enjoyable, non-technical, profound papers by very smart people are only given a “quickglance”.

Yes, that must be it. I feel embattled and angry. The fact is, a quick glance is more than the vast majority of the papers on the ArXiv get form me. There’s just too damn many of them, and only some percentage of them are about things I find interesting. This paper doesn’t particularly interest me because, generally, I have very little patience for philosophy in physics. As I said, I don’t think it is our place to say that an unknown theory “must” be anything. I just glanced at it this time because of this comment thread.

On the other hand, I do happen to believe that a final theory of quantum gravity will be background independent, so I don’t see where you’re getting that I’m going after Smolin on this point.

Has anyone in the string theory community systematically set forth some requirements or expected features of a background independent formulation of string theory? Should it be considered understood that M-theory will be the hoped-for background independent formulation, or is this a matter of disagreement?

M-theory is a dream, not really any particular theory. String theory really has been developed in a form of a bottom-up approach. No one has gone and said, “this is what we need from the theory; let’s put it in.” Rather, people have just explored more and more and various things have fallen out of the theory. The eleventh dimension, for example, came about from investigating the strong coupling limit of the IIA superstring.

The one real nonperturbative theory we have, AdS/CFT, seems to strongly depend on the asymptotics of the spacetime. This is somewhat of an in-between case: the only part of the background that is fixed is what happens at infinity. What happens in the middle is background independent. This has led a lot of people to think that perhaps that’s the best we’re going to be able to get.

One principle that a lot of people think will be important for some final theory of quantum gravity is the holographic principle. One expression of this is that the theory of quantum gravity will be encoded in some nongravitational theory in one less dimension. In AdS/CFT, the boundary is the holoraphic screen, but in more general spacetimes, there will be other possible screens. Bousso has a proposal for this. Because this still fundamentally requires the idea of a real spacetime geometry, the principle is only semiclassical, but many people think that it will be a general feature of whatever form of emergent geometry appears in the end.

Really, it might be that the whole idea of background independence is a non sequitor. Geometry will arise only in some limit of the theory, and the fundamental theory will have some completely different set of degrees of freedom. As I said, I don’t think we get to tell the theory what to be. We’ll just have to see (hopefully in our lifetimes) how it turns out.

Hi meh,

It’s a rather young conference, with relatively few of the the organizers, speakers and participants in their fifties or sixties. I’m kind of slumming here, since I’m not an expert in algebraic geometry, but I do notice that the people here include quite a few of those my department identified as the best young people in the field in internal discussions about who to try and hire.

Smolin’s characterization of modern theoretical struggles, as really only a continuation of the old debate on the true nature of space and time, is not explicitly recognized very often these days, but I think it’s right on. However, if the reason why string theory cannot meet the challenge of the landscape is that there is no background-independent formulation of it, then what does that imply for

anybackground-dependent theory?Juan Maldacena just posted a comment on Cosmicvariance stating his enthusiastic support for the study of the landscape. However, Smolin’s argument that because the static probability distributions live on the “space of possible backgrounds,” and the dynamics of the theory are to be done on this space, and thus must employ a fixed background in the study of the landscape, makes this effort an illogical endeavor, and he calls for “an alternative methodology for treating [it]”

Nevertheless, his alternative is not a background-independent formulation of string theory, but a background-independent quantum theory. I think this is very significant, because, as he points

out, the reason string theory fails is because it is background-dependent, which is what helps make it untestable and less explanatory, while background-independent theories are “more constrained” and therefore more “subject to law.”

Ironically, then, this implies that the strenuous opposition to string theory found on this and other blogs appears to be a little like someone throwing stones while living in a glass house, doesn’t it? I mean, if background-dependence is an indictment of accepted physical theory in general, which Smolin seems to think it is, then the sociological pathology, identified as the maddening fascination with string theory that so many physicists are caught up in, with the accompanying refusal to recognize its futility, turns out not to be due to the philosophical error of the misguided, pursuing a non-falsifiable theory, but the epistemological error of all of us, perpetuated now for generations.

This error is the assumption that we “know” what reality is, and that the grand edifice that has taken centuries to build, and that is built upon the assumption that space and time are non-dynamical structure, or even partly dynamical structure, is unassailable, is doing us in, just as surely as the old farmer was done in by his false assumptions.

As I have pointed out before, Einstein warned us of this very peril. Epistemologically speaking, assuming forces can exist autonomously, apart from the underlying motion from which they must proceed by definition, just because we cannot find such motion, is the fundamental error that has lead to the present predicament, because force requires a fixed background. Fields must evolve over time. Taking force out of the picture of gravity separately, by making the background partly dynamical, just avoids the issue in GR.

The fact is, gravity is a force, and as such must be the property of an underlying motion, but gravitational force is one that cannot be defined in terms of a quantum field on a fixed background of three space, for reasons that are clearly related to dimensions of the motion involved. But, unfortunately, since we think we know what space and time are, we can only talk in terms of the one-dimensional motion of objects “through” spacetime. Oh well.

Ironically, recognizing our errors in the understanding of the nature of space and time opens the door to formulating a truly background-independent theory, which is what we need, but how are we going to go that far back now?

It is unlikely that ST possesses a background-independent formulation. Lee Smolin has informed me that a rigorous theorem rules out anomaly-free Fock quantization of background-independent theories, and I see no reason to doubt that. This explains why the conflict between LQG and ST is so fierce. ST gives up background independence, which to LQGists is the most profound lesson from GR,

and LQG gives up Fock QM, which string theorists can never accept. Hence the conflict will persist.

The loophole is that you can combine Fock QM with background independence, provided that you give up anomaly freedom. Most people think this idea is absurd, since classically a gauge symmetry is a redundancy of the description. However, there are examples where quantum anomalies break gauge symmetry, without violating unitarity. The subcritical free string is the best known example. This example is of course also very relevant to QG, since the free string is nothing but 2D gravity coupled to scalar fields.

the paper is enlightening in general but doesn’t treat CDT adequately.

CDT is more background independent than LQG (independence is not an all-or-nothing feature of theories, there are degrees)

Smolin schematizes degrees of background independence and discusses striving for a greater extent of independence as a strategy. but his paper does not acknowledge that dimension becomes a dynamical variable in CDT rather than being determined in advance as it is in LQG.

It is unlikely that ST possesses a background-independent formulation. Lee Smolin has informed me that a rigorous theorem rules out anomaly-free Fock quantization of background-independent theories, and I see no reason to doubt that.I’m not sure I want to steal someone else’s thunder, but I have heard that one of the premises of that theorem is seriously flawed.

Thomas Larsson: It is unlikely that ST possesses a background-independent formulation. Lee Smolin has informed me that a rigorous theorem rules out anomaly-free Fock quantization of background-independent theories, and I see no reason to doubt that.

Aaron:

I’m not sure I want to steal someone else’s thunder, but I have heard that one of the premises of that theorem is seriously flawed.Aaron, you’ve gotten me curious. Could you please be more specific? What theorem has the questionable premise? What is the premise and in what way is it flawed?

I’ve been under the impression that the theorem requires a sort of quantization that doesn’t even apply to ordinary gauge theories, but I haven’t looked at it — I don’t even know the reference — so I’d rather not pontificate too much on it.

“

It is unlikely that ST possesses a background-independent formulation.”Yes, M-theory is not so simple as a nonperturbative version of ST. It is something different (there the new name) that is not based in the old string theory framework. This is the reason that nobody formulate still M-theory.

M-theory is not a dream, it is the last hope for some guys ðŸ™‚

But string community is not being sincere. Since there exist not M-theory (matrix formulation does not work), it looks like a blanck paycheck.

Next the formula of everything

” ” = ” ”

that i discovered today. You can verify by yourself that reduces to M-theory in the joke regime (i.e. when jokes –> infinite).

Would string theorists not explain to public that after of 30 decades of futile efforts finally we know that

string theory will be not the final theoryand theoreticians need of a new theory that nobody (including Witten) know what is?Uppps!

I mean 3 decades!!

Well exactly are already 4 (or 38 years).

Motl wrote 12 pages on his blog about the new Smolin paper and, I thought, missed the point. Here in these comments we havent even restated Smolin’s main message.

He announces this quite explicitly in italicized passages at the beginning and then at the end (with reference to the previous) so it’s difficult to overlook.

–quote from Smolin introduction–

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.This essay is written with the hope that perhaps some who have avoided thinking about background independent theories might consider doing so NOW.

–end quote–

I have added the emphasis on the word NOW which I think is an essential part of the message. It is friendly advice. Should not raise the hackles of sensitive string theorists. It is trying to be constructive and reasoned. And it is urgent. Theorists have been saying for years that the eventual string theory should be background independent—but have postponed such reformulation. He encourages them to go ahead with it—also gives examples of background independent theories suggesting possibility, and points to his own recent work towards a background independent formulation of M theory.

Then right at the end he comes back to this theme

–quote Smolin conclusions–

…The former are more constrained, hence harder to construct. More of what is observed is subject to law, as there is no background to be freely chosen. Hence, it appears that relational, background independent theories are more testable, and more explanatory.

This is the reason for my provocative hypothesis. If it is true then

the reason that string theory finds itself in the situation described in the introduction is that no background dependent theory could successfully solve the five key problems mentioned there. If this is true, then the only thing to do is to go back and work on the less studied road of relational theories.At the same time, I have tried here to explain the key problems still faced by the relational road…

–end quote–

Lubos Motl wrote a 12-page blog reacting to Smolin’s “The case for background independence” that you mention here, and it contains misleading statements like this:

—quote Motl—

On the other hand, there are no successes whatsoever of the approaches that Lee wants to call “non-perturbative approaches”. The main problem is that they don’t care about physics, experiments, and the new principles that are revealed by them; they prefer philosophical dogmas from the 16th century. It is a waste of time to discuss these “non-perturbative” speculations in detail. In all cases (causal set theory, loop quantum gravity, triangulation models), the speculations are based on the naive picture of space as being composed of infinitely sharp points – like in the classical theory – which are moreover exactly discrete. All these approaches make incredibly strong assumptions about the physics at the Planck scale whose probability to be incorrect safely exceeds 99.9999999999%; all of them belong to the discredited category of “gravitational aether theories”…

—end quote—

This is at the end of the section “Background Independence of GR” right before the section “Background independence in string/M theory”.

The nonperturbative QG approaches Smolin focused on and devoted sections of the paper to were Loop, Causal Sets, and CDT (currently the leading triangulations method).

Lubos blanket statement about spacetime discreteness in the nonperturbative approaches is in contrast to what the CDT developers say. They explicitly say they have found no evidence of spacetime discreteness or a minimal distance scale. So Motl is attributing to them what they neither postulate nor find as a result.

To illustrate, this from the introductory section, page 2, of a recent CDT paper hep-th/0505113

“The alternative we will advance here is based on new results from an analysis of the properties of quantum universes generated in the nonperturbative and background-independent CDT (causal dynamical triangulations) approach to quantum gravity. As shown in [5, 6], they have a number of appealing macroscopic properties: firstly, their scaling behaviour as function of the spacetime volume is that of genuine isotropic and homogeneous four-dimensional worlds. Secondly, after integrating out all dynamical variables but the scale factor a( ) in the full quantum theory, the correlation function between scale factors at different (proper) times is described by the simplest minisuperspace model used in quantum cosmology. We have recently begun an analysis of the microscopic properties of these quantum spacetimes. As in previous work, their geometry can be probed in a rather direct manner through Monte Carlo simulations and measurements.

At small scales, it exhibits neither fundamental discreteness nor indication of a minimal length scale.”Also it is misleading to say as Motl does, that “

All these approaches make”incredibly strong assumptionsabout the physics at the Planck scale whose probability to be incorrect safely exceeds 99.9999999999%This evokes the canard that nonperturbative approaches are somehow wedded to precisely one version of the Einstein Hilbert action and cannot modify the action by additional terms. In CDT, to take one example, researchers are free to explore modifications of the microscopic dynamics and do indeed perform (monte carlo) computational experiments involving different versions of the action.

I fail to see what is “incredibly strong” about their assumptions.

It may also be that Lubos blanket statement (which he applied to all three approaches discussed by Smolin) is inaccurate as regards Loop gravity, as well as CDT. It may also be wrong for Causal Sets, but I cannot tell about that because I don’t know much about that approach. Here I am using CDT to illustrate the misleading, over-the-top nature of his comments. They sound as if he does

doesn’t know what he is talking about and is foaming at the mouth.

What is it about Smolin’s central thesis (that it is now time for string/M researchers to get a background independent formulation together—that it is urgent given the present situation of string/M) — that disturbed Motl so much that he had to respond like this?

And why doesn’t he address the main thesis of Smolin’s paper, which is basically some friendly advice, coupled with the urgency?

To all interested folks in string theory/LQG.

here is a link to Lee Smoln’s video archived colloquiam at CFA.

http://cfa-www.harvard.edu/colloquia/spring05/smolin.html

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