Tuesday, June 26, 2007

Is Witten working on loop quantum gravity?

In this text, I would like to analyze the methods and logic of PW, a well-known critic of string theory, in one particular context.

Relevant sources for this article:
Frame: Monstrous symmetry of black holes
Frame: Witten's paper is out
Wrong: Assorted news
Musings: Report on Witten's talk
Witten: Preprint
Witten: PDF for his talk
This text will be exclusively dedicated to the analysis of the description of Witten's work by PW which I find rather incredible (see "Assorted news"):
  • Witten’s talk is entitled “Three-Dimensional Gravity Revisited” ... So, at least one talk there will be about a non-string theory approach to quantum gravity more along the lines of the LQG program.
Wow. ;-) The picture below is a refined version of a photograph by Chehak and symbolizes how sane, natural, and correct the statement of PW approximately is:

Let us start with a simple question:

Why does PW write such a statement that will be shown to be a flagrant absurdity?

Well, the answer is obvious. If you read his blog or his book, you will learn that he believes that decisions in science do reflect and should reflect the emotional power of authorities. Edward Witten is such an authority, even according to PW, which is why PW thinks that if he manages to convince others about his interesting "story" that Edward Witten has largely switched from string theory to loop quantum gravity, it will have a dramatic impact on the scientific community.

Well, I happen to think that if Edward Witten started to work on loop quantum gravity, as defined by the existing contemporary methods and standards of the loop quantum gravity community, it wouldn't mean that physics is undergoing a phase transition. Instead, it would simply mean that Edward Witten would be getting senile. We all admire him and love him, if you want me to say strong words, but he is still a scientist, not God.

There have been many cases in which his opinion had much weaker impact on other scientists than what I would have found appropriate. And there have been cases in which quite many people started to do things because Witten did. On the other hand, it's clear that if Witten were saying things that don't make sense and can't be used by anyone to do logically coherent research, no one sensible would listen to him.

The motivation of PW is clear so let us ask another question:

Is PW's statement true?

No, it's absurd. Let's start with a simple, sociological description of the situation that should be comprehensible to non-experts.

If you open the preprint, you will see that most papers that are being cited were written by string theorists. You will see names like Maldacena, Strominger, Kachru, Dixon, Ginsparg, Harvey, Dijkgraaf, Moore, Seiberg, Verlinde, Friedan, Shenker, Gukov, Maloney, Vafa, and, indeed, Witten, among many others. They are related to physics of conformal field theory, AdS/CFT correspondence, partition sums, black hole physics. Their results and methods are used throughout Witten's paper.

On the other hand, one paper about loop quantum gravity by Ashtekar is cited in a footnote on page 3 of Witten's preprint as a curiosity and no results from that paper or any other loop quantum gravity paper is ever used by Witten. That would be really impossible because all of these results are wrong. They're simply results of faulty math.

Even without a deeper knowledge of physics, the reader should be able to verify that Witten is not doing anything that is "more along the lines of the LQG program", as we were told by PW. But let us analyze some details a bit more carefully.

Spacetime dimension and loop quantum gravity

Witten talks about physics of three-dimensional gravity in the anti de Sitter space. Is that the same dimension as loop quantum gravity? The answer is No. Loop quantum gravity is only loop quantum gravity if the spacetime dimension is four.

Neither Witten nor any other sane physicist I know of thinks that it is possible to define four-dimensional or higher-dimensional gravity - i.e. general relativity - as a pure gauge theory in the same number of dimensions. Witten, just like other big shots, thinks that the loop quantum gravity people have no standards. Physicists like Witten, Gross, and others would never discuss loop quantum gravity in a polite company. It's been a polite standard to allow the loop quantum gravity people do whatever they want, and simply ignore them.

What we're talking here, in the context of Witten's recent work, is another possible reinterpretation of a gravitational theory - namely three-dimensional gravity - in terms of gauge-theoretical degrees of freedom, namely using something that has also been called Chern-Simons-Witten theory. Fine, so let's ask:

Is Chern-Simons-Witten theory equivalent to three-dimensional gravity?

We must realize that the bulk of this question is vacuous.

Three-dimensional gravity is very different from gravity in higher dimensions because it has no local excitations. Why? Because Einstein's vacuum equations, namely Ricci flatness, imply complete flatness because in three dimensions, both the Riemann tensor R_{abcd} as well as the Ricci tensor R_{ab} have three independent components. These two tensors can therefore be calculated from one another. It follows that no gravitational waves are allowed. By quantizing this empty set, we obtain an empty Hilbert space of gravitons. There are no gravitons. There is no S-matrix to calculate. The situation is vastly less interesting than it is in four dimensions.

If there are no scattering amplitudes to calculate in this theory, what do we mean by the equivalence of two systems of equations both of which predict zero objects? Well, we mean that there must exist some other mathematical objects that can be mapped onto each other. Is it true?

Is Chern-Simons-Witten theory equivalent to three-dimensional gravity in some more general setup?

Sloppy physicists like to say Yes because at the classical level, one can make a field redefinition that changes the three-dimensional metric to a gauge field. Witten and more serious physicists have been explaining for quite some time that the answer at the quantum level is No. The Chern-Simons-Witten action and the gravitational action are not globally equivalent, they imply different ranges of path-integration, and absolute values from the gravitational action are not included in the Chern-Simons-Witten action.

Witten has also explained that the Kodama state, a popular formal solution of four-dimensional gauge theory occasionally employed for loop quantum gravity with a positive cosmological constant, is unphysical for a variety of reasons.

So is his new work finally confirming the LQG-like description?

The answer is "Just on the contrary." One of the main messages - or, using the words of Jacques Distler, the main message - of the work is that the gauge degrees of freedom simply don't give the right & full description of the quantum gravitational system.

The three-dimensional gravitational theory has no gravitons or other local excitations but it has black holes that macroscopically look like BTZ black holes. However, the precise quantum character of these black holes is not included in the Chern-Simons, gauge-theoretical description of the system. For example, the Chern-Simons gauge field gives us no hint that the black hole microstates transform as representations of the monster group, at least for some values of the curvature, even though this fact can be argued to be the case by other methods.

So Witten's point is really the opposite one than what PW wants his undemanding readers to believe: Witten argues that even in systems that can superficially be written in terms of bulk gauge fields and nothing seems obviously wrong - such as the case of three-dimensional gravity that predicts no light local excitations - the bulk gauge-theoretical description is always a bad language to talk about the theory at the quantum level.

The boundary conformal field theory whose existence is postulated via string-theoretical arguments always gives a more accurate description of the full quantum theory and the sloppy LQG-like formulae should never be viewed as the full story, not even in the cases where it's harder to show that they're inconsistent.

The three-dimensional anti de Sitter background is not connected with the ten-dimensional and eleven-dimensional vacua in any obvious way but such a fact never means that a given background is not a part of string theory: we already know a lot of islands where moduli are frozen which makes decompactification and other processes impossible. However, what's important is that the basic framework in which the physical laws are formulated and in which the observables are calculated and the consistency of the theory is deduced is the standard framework of string theory - including the AdS/CFT correspondence, one of the main topics of string theory in the last decade - and it has nothing whatsoever to do with loop quantum gravity as we know it.


You can see that one needs to write many kilobytes of text to carefully debunk vicious lies that PW can compress into one short sentence but I hope that it should now be clear to virtually everyone that these particular statements by PW are lies.

However, consider that PW has been intentionally generating tens of thousands of such lies on his blog for more than three years. Virtually everything he has ever written is junk and he's been probably preparing to do this dirty job for decades. And many people are so uneducated and uninformed that they are ready to buy some of these lies. If they don't buy all of them, 1% is enough because it is still hundreds of vicious lies.

You can't be surprised that using Bush's jargon from 9/11/2001, I think that we should make no distinction between the individual who generates these lies and those who harbor him. ;-)

And that's the memo.

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