Not Even Wrong

Recently I’ve been reading a new book, The Evidence for the Top Quark, by a philosopher of science named Kent Staley. It’s a combination of a history of the CDF collaboration’s work leading up to their claim to have discovered the top quark, together with an extensive discussion of issues in the philosophy of science raised by the different methods used to analyze the data. The book is very topical since last week the D0 collaboration published an article in Nature claiming a new, more accurate, mass for the top quark based upon a re-analysis of their data from Run I of the Tevatron, which lasted from around 1992-96. The old analysis of the D0 data gave a top mass of 172.0 +/- 7.1 Gev, the new analysis gives 179.0 +/- 5.1 Gev. Combining the D0 data with the CDF data, the old analysis gave 174.3 +/- 5.1 Gev, the new 178.0 +/- 4.3 Gev.

Measuring the top quark mass is quite tricky since there are not a lot of events to work with and one needs to precisely measure the energies of jets. If a linear collider ever gets built, it would allow much more precise measurements. Knowing the top quark mass accurately is very important for the following reasons:

1. In the standard model one can try and use precision measurements of the electroweak parameters to observe the effects of higher loops including the Higgs and get a prediction for the mass of the Higgs. This crucially involves the top quark mass, since that is the strength of the top-Higgs coupling and the top quark couples far more strongly to the Higgs than any of the other fermions. With the latest D0 value for the top quark mass, one now expects (95% confidence level) that the mass of the Higgs is less than 237 Gev. For more details see websites at CERN and Fermilab.

2. In the minimal supersymmetric extension of the standard model there is an upper bound on the mass of the lightest neutral Higgs, a bound that depends strongly on the top mass. There’s an explanation of this on Jacques Distler’s weblog. With the newest value for the top quark mass one expects that the Higgs mass should be below 140 Gev in the supersymmetric case.

There are a few funny things about this report from D0:

1. It was published in Nature rather than the more conventional Physical Review Letters. Nature is not where high energy experiments normally announce their results and this appears to be an attempt to get wider publicity than is usual for such a result. For some comments on this, see David Harris’s weblog.

2. The new method of analysis is similar to one discussed extensively by Staley in his book: the “dynamical likelihood method” due to Kuni Kondo. Ten years ago the CDF collaboration was rather skeptical of this method and decided not to use it, basically seeing it as too complex to be reliable. Have they changed their minds? Will CDF re-analyze its Run I data using this technique too?

3. Much is made in the paper and the associated Fermilab press release that this result changes the “best estimate” of the Higgs mass from 96 Gev (which is excluded by LEP results) to 117 Gev, which isn’t. While this sounds impressive, it would be a lot less so if you do what you are taught in high-school physics and quote error bars with your numbers. As mentioned above, while it is true that the new result is that 117 Gev is “most likely”, it is also true that a very wide range of values is almost equally likely. A more sensible but much less impressive way of saying things would be to just say that at 95% confidence level the Higgs mass has to be between about 50 and about 250 Gev.

Update: The D0 Nature article is now at the arXiv.

According to a press release from UCSB, three theoretical physicists have proposed “the most viable test to date for determining whether string theory is on the right track”. This is based on a paper about cosmic strings where the authors manage to cook up a highly unlikely scenario where large strings exist and produce gravitational radiation observable by LIGO in the next couple of years.

Normally in the English language, calling something a “test” of a scientific theory would indicate that if it doesn’t work the theory is wrong. When LIGO doesn’t see this effect in the next two years I kind of doubt that there will be wholesale abandonment of string theory.

From one of the comments here I see that the Bogdanovs have put the reports on their theses on the CERN document server. One should perhaps take these with a grain of salt given their source. For instance, I wouldn’t be surprised if some reports were missing.

I’ve always had some sympathy for the people who ended up on the Bogdanov’s thesis committees. It’s a difficult position to be in when you have to decide what to do with students who seem to be enthusiastic and have worked hard, but are very weak and have completed not very good theses. A not unreasonable thing to do under the circumstances is to do one’s best to find something of value in their work, and leave the job of keeping nonsense out of the literature to journal referees.

But the Bogdanov theses, especially Igor’s, were so full of egregious nonsense, in particular with respect to topological quantum field theory, that they should have been beyond the pale. While some of these reviewers were string theorists, others weren’t, so the whole mess can’t be blamed on string theory.

Louis de Branges is a mathematician at Purdue who has had a long history of claiming proofs of the Riemann hypothesis. His latest claim has lead to a press release from Purdue. The press release points to what seems to be an older manuscript by de Branges outlining some of the history of the Riemann hypothesis and his work on it. This also includes some history of his ancestors, and de Branges has taken to calling himself “Louis de Branges de Bourcia”. He more or less promises that if he wins the Clay million dollar prize for solution of this problem he would use it to restore the ruined chateau de Bourcia for use as a mathematical research institute.

The actual purported proof is here. One mystifying thing about it is that in the abstract and introductory paragraph it repeatedly refers to relations to quantum mechanics, but there seems to be nothing about this in the body of the paper. Weyl’s book on quantum mechanics and group theory appears in the references, but nothing in the text seems to refer to this.

de Branges has a checkered history as a mathematician, with several of his claimed proofs of the Riemann hypothesis and other problems turning out to be incorrect. On the other hand, he did produce a correct proof of one well-known problem, the Bieberbach Conjecture. In that case his initial manuscript was pretty impenetrable, but after he explained his ideas to a group of Russian mathematicians, they gave a more understandable version of the proof and it became clear that de Branges really did have a proof. It looks like this one may also take some major effort to see what he really has.

For more about de Branges and the Riemann hypothesis, see the recent popular book “The Riemann Hypothesis: the Greatest Unsolved Problem of Mathematics” by Karl Sabbagh. A review of this book has some interesting comments about de Branges and his NSF funding.

A couple weeks ago a preprint appeared on the arXiv by R. A. Arenstorf, a mathematician at Vanderbilt University, claiming a proof of the twin prime conjecture. I asked one of my colleagues who is an expert on the subject about it and he said he didn’t believe it and would bet $100 it was wrong. Today I see that Arenstorf has withdrawn the preprint, saying that a serious error has been found.

A couple years ago two French brothers, Igor and Grichka Bogdanov, managed to get Ph.Ds in France and publish several nonsensical papers about quantum gravity in refereed physics journals, several of them rather well-known and prestigious ones. John Baez has a useful web-page about this story.

This whole thing seemed to me strong evidence of how in recent years there has been a collapse of any real intellectual standards in this part of theoretical physics, and I ended up being quoted about this in various places. The “Affaire Bogdanov” died down fairly quickly, and the scandal doesn’t seem to have lead to much in the way of higher standards.

I recently heard from Fabien Besnard, who wrote to tell me that the Bogdanovs have a new book out, called “Avant le Big-bang” (Before the Big Bang), in which they quote me as endorsing their work. Besnard has a web-page (in French) on the latest developments in the L’affaire Bogdanoff.

The Bogdanovs wrote me last year, here’s a copy of their e-mail. I made the mistake of thinking “maybe these guys aren’t so bad, just overly-enthusiastic sorts who could use a little helpful advice”, and wrote this back to them. In their book they use part of my e-mail, mis-translating:

“It’s certainly possible that you have some new worthwhile results on quantum groups..” (I was being too polite here; while possible, it is unlikely)

as

“Il est tout a fait certain que vous avez obtenu des resultats nouveaux et utiles dans les groupe quantiques” (It is completely certain that you have obtained new worthwhile results on quantum groups).

One lesson from this is not to write back to crackpots. Another strange part of this story: late last year I received an e-mail purporting to be from a “Prof. L. Yang” at the “International Institute of Mathematical Physics” at Hong Kong University. It appeared to come from

th-phys.edu.hk

a domain name that is registered with the Hong Kong DNS, supposedly by the Hong Kong University of Science and Technology. I connected to the web-site at this address, which at the time contained an official-looking web-page for this Insitute. It now contains just a listing of directories, one of which is full of .pdf files of the papers of Arkadiusz Jadczyk.

This web-site is hosted by a US web-hosting company “Everyone’s Internet, Inc.” If you look carefully at the header for this e-mail you see that while it purports to be from

“liu-yang.imp@th-phys.edu.hk”

it really comes from

th-phys.edu.hk (ATuileries-117-1-27-138.w193-253.abo.wanadoo.fr [193.253.192.138])

which appears to be a machine connecting to the internet from Paris, set to claim to be “th-phys.edu.hk”.

It’s looking more and more like the original idea that the Bogdanovs were hoaxers, putting on the physics community, was closer to the truth than the idea that they are serious, just not very good, researchers.

Update: The comment section received a message from a supposed mathematician named “Roland Schwartz” defending the Bogdanov’s work on quantum groups. The source of the comment was
IP number 217.128.255.129. The DNS shows

nslookup 217.128.255.129

Name: ATuileries-117-1-29-129.w217-128.abo.wanadoo.fr
Address: 217.128.255.129

Funny, this seems to be a very close neighbor in Paris of Prof. L. Yang…..

I also just noticed that Jacques Distler has posted an account of his experiences with “Prof. L. Yang” et. al.

I was visiting the math department at Dartmouth the past couple days, and gave a colloquium talk there. It’s now available online.

Witten has contributed an essay to the latest issue of Nature about electroweak symmetry breaking. He describes the main conventional ideas about this, ending with the latest anthropic ones. Here are his comments about those:

“One approach is the anthropic principle, according to which the dark energy and the Higgs particle mass take different values in different parts of the Universe, and we inevitably live in a region in which they are small enough to make life possible. If so, many other properties of the Universe that we usually consider fundamental — such as the mass and charge of the electron — are probably also environmental accidents. Although I hope that this line of thought is not correct, it will inevitably become more popular if experiment shows that electroweak-symmetry breaking is governed by the textbook standard model with a Higgs particle and nothing else.”

He ends with the eminently reasonable summary:

“As yet, none of these theoretical proposals about electroweak-symmetry breaking are entirely satisfying. Hopefully, by the end of this decade, experimental findings at the Tevatron and the LHC will set us on the right track. But the diversity and scope of ideas on electroweak-symmetry breaking suggests that the solution to this riddle will determine the future direction of particle physics.”

Sean Carroll has some comments about the anti-big bang petition. He also points to Ned Wright’s explanation of what is wrong with various proposed alternatives to the big bang scenario. In particular this explains in detail what the problems with Irving Segal’s “Chronometric Cosmology” are, something I’d always wondered about.

Segal was a very good mathematician, who did serious work on quantum field theory in the 50s and 60s. He’s the “Segal” in what is sometimes called the “Segal-Shale-Weil” representation. Segal is a counter-example to Carroll’s observation that, for the most part, opponents of the big bang are not very smart. Unfortunately, it seems that quite smart and otherwise reasonable people can have unshakable faith in ideas that don’t work. Segal’s student John Baez wrote up some of his memories of his advisor and his cosmological research.

Slides used by many of the lecturers at the recent Davis mathematical physics conference in honor of Albert Schwarz are now online.