Not Even Wrong

A preprint by Andrei Marshakov and Antti Niemi appeared on hep-th this evening making a remarkable claim. According to this preprint, a few weeks before passing away recently at the age of 93, Shiing-Shen Chern completed a preprint entitled “On the Non-existence of a Complex Structure on the Six Sphere”.

Whether or not a given manifold defined using real coordinates can be given the structure of a complex manifold is often a difficult problem. For the case of a d-dimensional sphere, clearly you can’t do this in odd dimensions, but for even dimensions, you certainly can for the case d=2. For the cases d=4 and d=8 or more, there is a topological obstruction to even finding an “almost complex structure”. In other words, you can’t find a continous choice for each point on the sphere of what it means to multiply elements of the tangent space by the square root of minus one. The case d=6 is special: you can use the octonions to construct an almost complex structure, but this complex structure is not “integrable”, it doesn’t come from any local choice of complex coordinates. One of the most famous open problems in geometry has long been the following: is there another almost complex structure on the six-sphere that is actually integrable?

It has long been conjectured that there is no such integrable almost complex structure, but no one has ever been able to prove this. Chern’s preprint contains a purported proof, but Marshakov and Niemi devote only a paragraph to the non-trivial part of his argument. From their preprint you can’t tell whether Chern has a valid argument.

I’ve heard via e-mail from a knowledgeable authority on the subject who points out that there are serious flaws in the manuscript that was privately circulated. His opinion is that Chern’s argument actually does prove something interesting, but not the full result Chern claims, so the conjecture about the non-existence of a complex structure on the six-sphere remains open.

Greg Moore has written an article for the latest Notices of the AMS entitled “WHAT IS… a Brane?”. He begins by noting that “The term ‘brane’ has come to mean many things to many people” and one of the difficulties of the subject is that one has to figure out from context what sort of brane someone is talking about.

For the case of branes of dimension greater than one, in general no one knows how to consistently quantize such objects. See Warren Siegel’s research summary for comments about this. He notes that now that M-theory shows that non-perturbatively strings are membranes in 11d, one doesn’t have a finite quantum theory of gravity, since membranes are infinite even in perturbation theory. All one has is an effective low-energy supergravity theory, which is what one had before one got involved with string theory. While at Siegel’s web-site, check out his latest parody paper called “The Everything of Theory”, which includes the following lines:

“The real problem with string theory is that there is no alternative. However, the reason there is no alternative is that no one ever bothers to look for one; in fact, there is a strong resistance to even considering looking for one. Consequently, practically all theoretical high energy physics (and even most of phenomenology) is now string theory. Thus, string theory is not so much the Theory of Everything (since it explains nothing), but rather the “Everything of Theory”, since it now encompasses all of theory. This era in string research is strongly reminiscent of the Dutch tulip trade just before the Tulip Crash of 1637. ”

I, for one, am missing the joke here…

For some new hyping of a different kind of brane, see the latest Nature, which has a piece on Nima Arkani-Hamed. Equal time is given to LQG, with a similar piece on Martin Bojowald.

Update: Lubos Motl has a long posting about branes and M-theory, which explains many things. As usual though, he insists that the full dynamics of the branes in M-theory is completely determined and unique even though he doesn’t know what it is in any phenomenolgically realistic background. To get a finite quantum theory of gravity that has anything to do with the real world out of M-theory, you need to show that you can get well-defined, finite results for the dynamics of these branes in the case of four large dimensions, the rest small. As far as I can see any claim to have this now is purely wishful thinking.

Several people wrote in this morning to tell me about Phil Anderson’s comments about string theory that appeared in the New York Times today. These originally come from John Brockman’s “Edge” web-site where he has gathered responses from more than a hundred scientists and others to the question “What do you believe is true even though you cannot prove it?”.

Beside’s Anderson’s answer, also interesting is Paul Steinhardt’s. Steinhardt refers to the currently fashionable use of the anthropic principle as “an act of desperation” and “millennial madness”, notes that the Weinberg anthropic “prediction” of the cosmological constant gives the wrong value, and even acknowledges that string theory may just be wrong. For sheer weirdness, as usual these days, Lenny Susskind is hard to beat. Brockman doesn’t seem to have located any string theorists who believe string theory but can’t prove it. Since it can’t be proved, I guess even they don’t believe it anymore.

Phil Anderson has always been somewhat of an intellectual hero for me. He’s really the person who discovered the Higgs mechanism, among many other things. Despite a reputation for being a curmudgeon, at one point he was quite kind to me. At some sort of social event at Princeton to mark students passing their generals, he came up to me and told me that he had graded my solid state physics exam. He complimented me on one problem in particular, one I had got wrong. I had realized something was wrong with my solution of that problem, noting on my exam that the result I was getting couldn’t be right and explaining why. He told me that this had impressed him, that one should always know what the result of a calculation should look like before attempting it.

I haven’t posted anything new here in a while, with the holidays and trying to get over a bad cold keeping me otherwise occupied. Partly because of this the comments section has been to some degree taken over by people who want to discuss things I have no interest in. I’ll try and put up something new soon (comments on Penrose’s new book), but I did want to make some remarks about the problem of crackpotism in theoretical physics, something which is especially a problem for open forums on the internet like the comment section here.

When I first started studying particle physics during the 1970s, it was pretty clear to me how to tell the difference between serious people and crackpots. The Standard Model had just recently been formulated and it had started to accumulate an impressive amount of experimental evidence in its favor. So, at least in particle theory, serious people were doing one of a small number of things. The more phenomenologically inclined were analyzing the new experimental results to see if they further validated the Standard Model, or suggesting new experiments that would test different parts of the model. More mathematically inclined sorts were trying to understand the rich structure of the model, trying to get a better grasp of its aspects that were still poorly understood. People inclined to speculation were working on ambitious extensions of the model, hoping to find something compelling that would both explain some of the model’s parameters and make new, testable predictions.

So, to my mind, crackpots were those claiming to have new ideas about particle physics, but refusing to really engage in some way with the Standard Model quantum field theory. There were plenty of them around, including S-matrix die-hards like Fritjof Capra, those who wanted to go on about what happened before the big bang and how that explained all properties of particles, and a wide variety of people with their own private TOE that completely ignored the Standard Model. All you had to do was learn to ignore such people.

During the last 20 years, distinguishing crackpots has become a lot tougher, and it has gotten much more difficult recently. Famous professors from the best research institutions in the world go on about the properties of the universe being determined by colliding branes, or by an anthropically determined point in a multiverse, or any number of similar ideas. The dominant idea in the whole field makes nothing like what would normally be considered a testable scientific prediction, and those pursuing it don’t seem too bothered by the increasing evidence that this situation will never change. Personally I haven’t much changed my criterion for crackpotism in particle physics: if someone is not engaging in a deep way with the Standard Model and/or the kind of mathematical structures it involves, they’re probably a crackpot.

When I first wrote a critical article about string theory and made it public about four years ago, I got quite a lot of reaction. Almost all of it was gratifyingly positive, but I ended up hearing from quite a few people who were convinced that since I didn’t like string theory, surely I would like their alternative. These alternatives spanned a wide range, from very serious work to complete crackpotism, including all shades of in-between. The one thing that caused me to worry that there might be something wrong with my criticisms of string theory was the nature of a small number of my supporters. Some of these people still write to me regularly, and my e-mail is full of crazier things than what appears in the comments on the weblog. It’s embarassing to get cc’d on an e-mail to a long list of very prominent physicists by someone who is quoting my criticisms of string theory to back up their own even sillier ideas.

I’ve gotten very good at hitting the delete key or, in extreme cases, using procmail to automatically filter this stuff out of my inbox. I suggest similar tactics in reading the comment section here. The first line of defense against people who you think are not making any sense is just to ignore them. Do not give in to the temptation to point out to them that they are not making sense, because all this will accomplish is to clutter things up as they respond to your response to them.

I’m not about to start just deleting comments that I think are of a crackpot nature, partly because it is now hard to set up a clear criterion for what is crackpotism (should I delete Lenny Susskind’s comments if he decides to write in some day?). But to the extent that the volume of off-topic comments starts to overwhelm those that are interesting and related to the postings, I will have to take some sort of action. If you are posting large numbers of comments, mostly far off the topic at hand, please stop doing it now. If you are responding to such off-topic comments, please stop doing that too, don’t encourage them!

Now for some comic relief:

A new issue of the Notices of the AMS is out. It contains an entertaining article entitled Foolproof: A Sampling of Mathematical Folk Humor with many examples of mathematical humor. Physicists also put in an appearance.

There’s an interview with Andy Strominger in the Calcutta newspaper The Telegraph. Strominger was presumably in India for the string theory conference there this past week.

The thing I found interesting about the interview was how skeptical the interviewer was, repeatedly asking about whether string theory might not be wrong. Perhaps at least some members of the media are starting to get a clue.

I was wondering why there were lots and lots of hits on this weblog today coming from Google searches for “first evidence for string theory”. It looks like the answer is this lead article from the latest New Scientist magazine. I don’t have access right now to the full article, but it’s clearly based on the usual cosmic string hype. After all, according to the author, string theory “is our best hope of understanding how the universe works”, so anytime astronomers see something unusual, what else could it be but a string?

Update: I finally got ahold of a copy of the full article. It is based on two separate anomalies seen by astronomers. The first is called “CSL-1”, which was first reported nearly two years ago. It appears to be two nearly identical galaxies right next to each other, but the authors of a paper about it would like to believe there is some inter-galactic cosmic string producing two images of a single galaxy via gravitational lensing. Even if you believe this, there’s no evidence this is a fundamental superstring, even Joe Polchinski doesn’t think so (see Lubos Motl’s excited posting about “astronomers prove string theory”).

The second observation actually has nothing to do with the first (despite what the opening sentences of the story suggest). It’s of a quasar called Q0957+561A,B that really is a gravitationally lensed object. One thing I don’t understand is that in the case of CSL-1, the fact that there are only two images is taken as evidence that a string is doing the lensing (and claims are made that lensing by point like objects only produces odd numbers of images), whereas for Q0957+561A,B there are only two images, but an intervening galaxy, not a string, is what is doing the lensing. For the quasar pair, some changes in brightness by about 4% have been observed, so it has been suggested this is due to a nearby cosmic string (inside our galaxy, within 10,000 light years) which is moving around in our line of sight with the quasar pair.

I’d be curious to hear what professional astronomers think of this. To me it looks like just more string theory hype, and I now suspect that for the indefinite future, whenever an astronomer somewhere, somehow sees something anomalous, we’re going to be subjected to claims that “strings have been observed!!”.