“So what will you do if string theory is wrong?”

In a new preprint of an article entitled “So what will you do if string theory is wrong?”, to appear in the American Journal of Physics, string theorist Moataz Emam gives a striking answer to the question of the title. He envisions a future in which it has been shown that the string theory landscape can’t describe the universe, but string theorists continue to explore it anyway, breaking off from physics departments to found new string theory departments:

So even if someone shows that the universe cannot be based on string theory, I suspect that people will continue to work on it. It might no longer be considered physics, nor will mathematicians consider it to be pure mathematics. I can imagine that string theory in that case may become its own new discipline; that is, a mathematical science that is devoted to the study of the structure of physical theory and the development of computational tools to be used in the real world. The theory would be studied by physicists and mathematicians who might no longer consider themselves either. They will continue to derive beautiful mathematical formulas and feed them to the mathematicians next door. They also might, every once in a while, point out interesting and important properties concerning the nature of a physical theory which might guide the physicists exploring the actual theory of everything over in the next building.

Whether or not string theory describes nature, there is no doubt that we have stumbled upon an exceptionally huge and elegant structure which might be very difficult to abandon. The formation of a new science or discipline is something that happens continually. For example, most statisticians do not consider themselves mathematicians. In many academic institutions departments of mathematics now call themselves “mathematics and statistics.” Some have already detached into separate departments of statistics. Perhaps the future holds a similar fate for the unphysical as well as not-so-purely-mathematical new science of string theory.

This kind of argument may convince physics departments that string theorists don’t belong there, while at the same time not convincing university administrations to start a separate string theory department. Already this spring the news from the Theoretical Particle Physics Rumor Mill is pretty grim for string theorists, with virtually all tenure-track positions going to phenomenologists.

I have some sympathy for the argument that there are mathematically interesting aspects of string theory (these don’t include the string theory landscape), but the way for people to pursue such topics is to get some serious mathematical training and go to work in a math department.

The argument Emam is making reflects in somewhat extreme form a prevalent opinion among string theorists, that the failure of hopes for the theory, even if real, is not something that requires them to change what they are doing. This attitude is all too likely to lead to disaster.

Update: A colleague pointed out this graphic from Wired magazine. Note the lower right-hand corner…

Update: Over at Dmitry Podolsky’s blog, in the context of a discussion of how Lubos’s blog makes much more sense than this one, Jacques Distler explains what it’s like for string theorists these days trying to recruit students:

Unfortunately, I’ve seen a number of prospective graduate students, who spent their undergraduate days as avid readers of Woit’s blog, and whose perspective on high energy physics is now so hopelessly divorced from reality that the best one can do is smile and nod one’s head pleasantly and say, “I hear the condensed matter group has openings.”

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Anonymity at Cosmic Variance

Over at Cosmic Variance, anonymous comments personally attacking me have been posted recently by someone who identifies themselves only as “string theorist”. I’ve complained to Sean Carroll and his colleagues about their policy of allowing the comment section of their blog to be used for anonymous ad hominem attacks by physicists who are unhappy with Lee Smolin and me because of our criticism of string theory. If someone wants to argue not about science, but to complain about my behavior, I’m perfectly willing to engage in such a discussion, as long as it’s with someone who is willing to take responsibility for their own behavior.

Here’s the response I received from Sean:

Personally, I could not care less whether a comment is anonymous or signed. It just makes no difference to me. I understand that you feel otherwise, as you have said so over and over and over again. I will delete comments if they are vulgar or overly obnoxious, but anonymity is completely beside the point. If my co-bloggers feel differently, they are welcome to overrule me.

So, I guess if you want to anonymously attack, insult or slander people you disagree with about a scientific issue, Cosmic Variance is open for business.

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Creutz On Rooting

Michael Creutz has a remarkable new preprint out this evening, entitled The Saga of Rooted Staggered Quarks. It explains what has been going on in a rather bitter controversy within the lattice gauge theory community over the last few years.

While lattice gauge theory provides a quite beautiful way of discretizing gauge fields, preserving their geometric significance, fermions have always been much more problematic. Here the geometry is spin geometry, which doesn’t appear to have a natural formulation on a lattice. What does have a natural formulation is not a spinor field S, but End(S), the linear maps from S to itself, which can be identified with the exterior algebra, and naturally put on the lattice by assigning degrees of freedom to points, 1-simplices, 2-simplices, etc. The problem is that if you do this, you don’t get a theory of a single fermionic field, but instead multiple copies. This geometrical argument is just one aspect of the problem, which appears in other more convincing ways, but this all adds up to making chiral symmetry especially problematic on the lattice.

There are many possible ways of dealing with this, but one popular one has been “rooting” some of the fermionic degrees of freedom that have been staggered on neighboring vertices of the lattice. One ends up with four copies of what one wants, so the argument has been that the thing to do is to take the fourth root of this to get a calculation that tells one about a single fermion. The problem is that this is a quite non-analytic thing to do, and it is not clear that it gives one something sensible. A debate between Creutz and people using this method has raged for the last few years, with Creutz claiming that the rooting procedure gives the wrong answer, while proponents of rooting argue that the problems involved will go away in the continuum limit.

Creutz’s preprint describes the conclusion he has been led to about this, and his problems getting some of them published:

This led me to question whether there was some physical measurement one could make to determine if a quark mass was indeed zero. I could think of none, and proposed that a single vanishing quark mass might not be a physical concept. This paper was submitted to Physical Review D.

This is where the shit started hitting the fan. There was a common lore that if the up quark mass were to vanish, then the problem of why theta appeared to be phenomenologically very small would be solved. I was saying that this lore might be wrong. This drove the referees nuts, with statements like “I am somewhat concerned that the errors are so obvious.” After numerous similar scathing remarks the paper went to a divisional editor for PRD, who upheld their opinion. On rejection I took the paper and split it into two parts, one on the phase diagram and the second on the vanishing mass issue. These both appeared in Physical Review Letters, Phys.Rev.Lett.92:201601,2004 (hep-lat/0312018) and Phys.Rev.Lett.92:162003,2004 (hep-ph/0312225). I do derive some visceral pleasure from having turned a rejected PRD paper into two PRL’s…

Eventually the claims of the staggered advocates became so outrageous that I felt I had to be more aggressive. I was pushed further by statements that if someone had issues with staggered quarks, they needed to write them up. At the time I was too naive to appreciate how the stubborn nature of some personalities involved would mean that these arguments would be dismissed without serious discussion. As with the up quark mass issue, this is one of those situations where a person without tenure would be ill advised to challenge conventional lore.

So I submitted a paper (hep-lat/0603020) pointing out the inconsistencies between rooting and the expected chiral behavior. This was quickly rejected by PRL which has a policy of not publishing interesting and controversial papers. After transferring it to PRD, things got stuck, with numerous referees simply refusing to respond. After about a year and eight referee reports, some positive and some negative, PRD decided that they don’t publish interesting and controversial papers either. I did not take this delay kindly and rewrote the paper with the provocative title “The evil that is rooting.” This was fairly quickly accepted by Physics Letters (Phys.Lett.B649:230-234,2007; hep-lat/0701018), although the title was mollified at the editor’s suggestion…

The staggered community has continued to ignore these problems. I feel their stranglehold on the US lattice effort approaches scientific dishonesty. As an example of the prevailing vindictiveness, a recent paper of mine on a completely different topic was rejected from a prominent US journal on the basis of a single negative referee report stating that “It is puzzling that the author ignores all these highly relevant lessons that have been learned long ago in the context of the staggered fermion formalism.” It was overlooked because I wanted to avoid the ongoing controversy, of which the referee was certainly aware. After I did add remarks on the comparison with staggered, the paper was rejected without further review by a divisional associate editor representing the staggered community. He raised some symmetry issues based on comments by the Maryland group, to which I was never given a chance to respond. This paper was then submitted to a European journal where I hoped for a more equitable treatment. There it was quickly published.

Beyond the international ridicule this this controversy brings on the USQCD community, other aspects are particularly upsetting from a scientific point of view. First, enormous amounts of computer time continue to be wasted on generating lattice configurations from which any non-perturbative information will be questionable. About 38 percent of the current computer time allocated by the USQCD collaboration is going to continue these efforts. Second, young people associated with this project are taught to repeat, without question, the party line that all will be okay in the continuum limit. Third, the practitioners are such a powerful force that most outsiders are unwilling to look into the problems despite the fact that the underlying physics is so fascinating. And finally, I find it extremely unsettling that some physicists widely regarded as experts in chiral symmetry and lattice gauge theory can so casually and thoroughly delude themselves with bad science.

In short, the lattice has been very good to me. It is extremely painful to see it abused so blatantly

One would like to think that this issue will get sorted out over time as more work makes it clear whether or not rooting is as serious a problem as Creutz thinks it is. But the progress of science is not always smooth…

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This and That

The interactions.org web-site has a new useful feature, Interactions Blog Watch, which aggregates links to recent physics-related blog entries. One of the older such aggregators I know of is Mixed States, but it seems to have stopped on March 15. There’s also Jacques Distler’s Planet Musings, where he continues his efforts to pretend “Not Even Wrong” doesn’t exist.

Vanity Fair seems to think that the right person to review a book about Isaac Newton is Christopher Hitchens. Hitchens devotes much of the piece to condemning Newton as “a crank and a recluse and a religious bigot” who “spent much of his time dwelling in a self-generated fog of superstition and crankery.” He feels the same way about most scientists before the modern era, noting that:

It may not be until we get to Albert Einstein that we find a true scientist who is also a sane and lucid person with a genial humanism as part of his world outlook—and even Einstein was soft on Stalin and the Soviet Union.

He ends the piece by accusing Newton of doing everything he could to keep people from understanding the universe, and claiming that this was typical of physicists until recently, when physics began to become indistinguishable from the humanities:

Newton was a friend of all mysticism and a lover of the occult who desired at all costs to keep the secrets of the temple and to prevent the universe from becoming a known quantity. For all that, he did generate a great deal more light than he had intended, and the day is not far off when we will be able to contemplate physics as another department—perhaps the most dynamic department—of the humanities. I would never have believed this when I first despairingly tried to lap the water of Cambridge, but that was before Carl Sagan and Lawrence Krauss and Steven Weinberg and Stephen Hawking fused language and science (and humor) and clambered up to stand, as Newton himself once phrased it, “on the shoulders of giants.”

Hitchens doesn’t mention Michio Kaku, who has a new book out The Physics of the Impossible, which is on the New York Times bestseller list with the blurb:

A theoretical physicist who is one of the founders of string theory discusses the possibility of phenomena like force fields, teleportation and time travel.

The notion that Kaku is a “founder of string theory” seems to be becoming very widespread in the media.

Over at Cosmic Variance, Sean Carroll and various of his anonymous commenters are upset that Lee Smolin made it onto a list of Top 100 Public Intellectuals, with some suggesting that Kaku deserves to be there instead.

Finally, the latest Newsletter of the European Mathematical Society has the second part of an interview with Alain Connes, who has many interesting things to say:

they [theoretical physicists] work in huge groups and the amount of time they spend on a given topic is quite short. At a given time t, most of them are going to be working on the same problem, and the preprints which will appear on the web are going to have more or less the same introduction. There is a given theme, and a large number of articles are variations on that theme, but it does not last long…

The sociology of science was deeply traumatized by the disappearance of the Soviet Union and of the scientific counterweight that it created with respect to the overwhelming power of the US. What I have observed during the last two decades since the fall of the USSR and the emigration of their scientific elite to the States is that there is no longer a counterweight. At this point, if you take young physicists in the US, they know that, at some point, they will need a recommendation written by one of the big shots in the country, and this means that if one of them wants to work outside string theory he (or she) won’t find a job. In this way there is just one dominant theory and it attracts all the best students.

I heard some string theorists say: “if some other theory works we will call it string theory”, which shows they have won the sociological war. The ridiculous recent episode of the “exceptionally simple theory of everything” has shown that there is no credibility in the opponents of string theory in the US. Earlier with the Soviet Union, there was resistance. If Europe were stronger, it could resist. Unfortunately there is a latent herd instinct of Europeans, particularly in theoretical physics. Many European universities, at least in France or England, instead of developing original domains as opposed to those dominant in the United States, simply want to follow and call the big shots in the US to decide whom to hire…

I don’t think that we see similar things in mathematics, so there is a fundamental sociological difference between mathematics and physics. Mathematicians seem very resistant to losing their identity and following fashion…

In physics I adore reading; I spent about fifteen years studying the book of Schwinger, Selected Papers on Quantum Electrodynamics. He collected all the crucial articles, by Dirac, Feynman, Schwinger himself, Bethe, Lamb, Fermi, all the fundamental papers on quantum field theory, those of Heisenberg too, of course. This has been my bedside book for years and years. Because I have always been fascinated by the subject and I wanted to understand it. And that took a very long time to understand.

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Experimentalists 1, Theorists 0

At Fermilab the Tevatron is producing record amounts of luminosity, see here for a story about a celebration of this. Things also appear to be going well at the LHC, as the cooldown remains on schedule, and only a tolerable number (12) of PIMs needed to be replaced in the sector recently warmed back up. See here and here for some discussion of current planning for the next year. The machine should be cool and ready for beam commissioning in late June, and if all goes well, by September an initial physics run with 5 TeV beams at relatively low luminosity may begin. At these luminosities and energies, the stored energy in the LHC beam will be no greater than at the Tevatron (although the important number for physics, the per-particle collision energy, will be 5 times higher). The plan is to run until December, with a heavy-ion run at the end, then shutdown until April 2009. During the shutdown the magnets will be trained, allowing beams at the full energy of 7 TeV during the 2009 run.

Particle theory, especially string theory, is not doing as well. Data recently compiled about top-cited particle physics papers from 2007 shows only one [note added: should specify string theory here, at 27 and 31 are phenomenology papers from 2002 and 2000] theory paper from this century making the list of 51 most heavily cited papers, and that was the KKLT paper which is referenced by all “landscape” and “multiverse” studies. The sad state of string theory has even made it deep into the popular consciousness. Last week’s episode of “The Big Bang” featured a brilliant young prodigy explaining to the particle theorist character that his work on string theory was a “dead-end”, due to the landscape problem. Even economists are dissing the subject:

Modern financial theory as applied ranks with string theory in physics as one of the greatest intellectual frauds of our time. Whereas the vacuous pretensions of string theory have finally been exposed (we now know that the theory never generated a single falsifiable prediction), those of “financial engineering” are just beginning to be exposed both in the press and in lawsuits alike.

At Santa Barbara, Jennifer Ouellette reports on a workshop about “how to come off better during TV appearances”:

Joe Polchinski (inventor of D branes in string theory, and one of the few permanent members at KITP) also agreed to be mock-interviewed, revealing a sly sense of humor in the process. For instance, asked if there was any controversy about string theory, he deadpanned, “Oh no. Everybody agrees that string theory is correct.” It cracked up the room.

This workshop unfortunately didn’t seem to include the advice to just say no when asked by TV producers to participate in a short stupid comedy skit making fun of science and scientists. See here, here and here, for reports on Wednesday’s “Root of All Evil” show from Comedy Central, which featured a mercifully short segment making fun of scientists as incomprehensible geeks. Participating in things like this does about as much to help the image of science and scientists as appearing on a Spike TV segment about the use of physics to determine whether women can crush beer cans with their breasts.

Given that things are going very well with the LHC, and badly with string theory, string theorists are doing the logical thing: advertising their activities with graphics of strings superimposed on a picture of the LHC. See here and here.

Update: Minutes from the LHC Installation and Commissioning Committee April 11 meeting are here. They include the exchange:

L.Evans asked if the cryogenics teams are still on track for having the whole machine at operating temperature in mid-June. S.Claudet replied that taking the figure of 6 weeks from room temperature to 2K, and allowing 2 weeks of cryo tuning, sector 45 would be ready for hardware commissioning in the first half of July.

This indicates that beam commissioning is likely to begin in July, not June.

Also discussed was what to do about possible stray plastic parts in the beam tube:

Any pieces of plastic would be vaporised by the beam so we should not delay start-up to search for these.

Update: Commentary on this posting from Lubos here, including

I am amazed by the people who deliberately keep on opening the pile of manure called Not Even Wrong – it must be due to a really nasty deviation of theirs that dwarves pedophilia.

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Multimedia and the Journal of Number Theory

I recently heard from David Goss, editor-in-chief of the Journal of Number Theory, that the journal is planning on introducing video abstracts for papers that they publish. Here’s his e-mail explaining this:

Dear Colleagues:

By now I believe that all of us have had the pleasure of watching a famous scientist or mathematician discuss their work on internet video. I have certainly done so myself and learned much. Indeed I can readily give a long list of mathematicians who I would very much like to view presenting the ideas behind their great works.

For example, it would be fabulous to watch a young Serre discussing the ideas behind FAC or GAGA; or a young Faltings discussing his solution on the Mordell Conjecture etc. I am sure that each of you can compile your own long list (and obviously not just papers on number theory!).

It is in this spirit that I suggested to Elsevier that all JNT authors be allowed to present a short (4 minutes max) “video abstract” of their accepted manuscript. Elsevier has kindly accepted this idea and is now quite excited about it.

The idea is very simple: When a paper is *finally accepted* for JNT, the author will be notified and given the option of putting up a video abstract — THIS IS ONLY FOR ACCEPTED PAPERS! The video will be watched to check for professionalism etc., and those videos deemed offensive will not be used (and the author sanctioned!). The video will then be linked next to the paper on the JNT website. Information on how to upload files, etc., will be on the JNT website by April 23, 2008.

Videoing virtually anything is now deeply a part of our culture as witness the rise of YouTube. In fact, we will be using YouTube itself temporarily until Science Direct is augmented to handle flash files (which I hope will be within a few months). The url is:

http://www.youtube.com/user/JournalNumberTheory

where there is a short video about these multimedia abstracts!

I expect the video to be very low key like the one on the above url. I also think that, frankly, it will be a fun thing to do after all the hard work producing an accepted manuscript! Certainly the technology to produce such videos is now ubiquitous worldwide.

It is important to note that ALL such videos will be archived by Elsevier and thus will be available for future scholars and mathematicians.

With a little thought one can see vast possibilities here: For instance a paper on the topology of elliptic curves could be proceeded by a short video of computer graphics narrated by the author etc.

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John Wheeler 1911-2008

News of the death of John Wheeler came yesterday, and many people have already written detailed, touching and informative pieces about the man, his life and scientific achievements. See for example here, here, and here. With Wheeler gone, physics loses one of its very few living contacts with the early days of quantum mechanics, since his career reached back to the early thirties when he went to study with Bohr.

My most extensive contact with Wheeler was surely through learning GR from the marvelous textbook he co-authored on the subject. By the time I got to Princeton as a student, he had recently left for the University of Texas, in order to evade Princeton’s mandatory retirement age policy. He still was a presence in the department though, returning to give talks (I remember one that was an advertisement for the importance of the notion of a complex: “the boundary of a boundary is zero!” was the slogan). My only conversation with him was at a meeting organized between graduate students and a visiting committee of people evaluating the department. I recall a very friendly older man who came up to talk to me, and listened attentively to my going on for quite a while about how things could be improved. Only after we had finished speaking and he had left did I realize who I had been talking to. My overwhelming feeling immediately was that if I had realized this earlier I’d have much more enjoyed keeping quiet and getting the chance to ask him a few questions.

Update: See here for another article about Wheeler, from the University of Texas. It includes the claim that “Wheeler was the first person to emphasize the importance of string theory”, which, as far as I know, has nothing to do with reality.

Update: For more about Wheeler, see this interview just put on-line, and this discussion at Bloggingheads.

Posted in Obituaries | 21 Comments

Dark Matter

Yesterday evening I went to see the new film Dark Matter, which opened here in New York this weekend. In many ways, it’s very good, much better than I was expecting.

The plot is loosely based upon the story behind the 1991 shootings at the University of Iowa physics and astronomy department. Gang Lu, a Chinese graduate student who had recently defended his Ph.D. but was having trouble finding a job, shot and killed five people, including his advisor, and severely wounded a sixth person. One unfortunate aspect of the movie is that it rewrites this true story to make the killer much more sympathetic, while making some of the people who were murdered much less so than they seem to have been in real life. The families and friends of the victims may be justly outraged by this. There’s more about the film and the controversy over its relation to the Gang Lu story here.

In the movie the real life space physics at Iowa has been transposed to cosmology at a university in Utah. It remains set in the early 1990s, with protagonist Liu Xing recently arrived in the US from mainland China. His advisor, Jacob Reiser, is a cosmologist with a model called the “Reiser model” which is based on cosmic strings. Liu Xing comes up with what he considers a breakthrough, a new model based on using superstrings to explain dark matter. This doesn’t meet with Reiser’s approval, and he is failed at his dissertation defence for a bogus reason (this is one of the ways the movie sadly departs from a realistic plot or the true story). The scientific advisor for the movie was David H. Weinberg, a cosmologist at Ohio State, and Lee Smolin is thanked among many others in the credits.

The strongest point of the movie is its portrayal of the lives of the graduate students, mostly Chinese, who are struggling to adapt in an alien environment, some of them consumed with a passion to make breakthroughs in science, others already trying to figure out what to do about their not-so-great academic job prospects. The director, Chen Shi-Zheng, emigrated to the US about the same time as Gang Lu, 1987, and so starts from a deep understanding of what the experience of Chinese students arriving in the US at that time must have been like.

Back in the real world, David Harris is reporting from the big April APS meeting on the new Symmetry Magazine blog Symmetry Breaking. In a blog entry entitled Dark Matter Discovered? he reports a rumor that the DAMA collaboration will report on Wednesday that they have detected dark matter in the latest run of their experiment. This story just appears on Slashdot, “slashdotting” whatever unfortunate web-server is running the Symmetry Breaking blog, so it is inaccessible for the moment [I take that back, it just reappeared].

Update: For more about the DAMA rumor from science writers at the APS meeting, see this blog entry from JR Minkel, and a characteristically detailed and informative posting from Jennifer Ouellette.

Update: There are now reports from the talk by Tommaso Dorigo and Alexey Petrov, and the slides are here. Sounds like this experiment is definitely seeing a signal with yearly variation, but it’s controversial whether this is due to dark matter or something else much less interesting.

Update: Yet more from the New York Times and Tommaso on this topic.

Update: Yet more skeptical commentary about DAMA here.

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Physicists On Tape

Over at the Center for Science Writings, John Horgan has started an interesting project of posting copies of taped interviews with scientists that he has accumulated over the years, starting with an interview with Chandrashekar. In a blog entry about this, he points to a piece entitled Revenge of the Science Writer from 2001 by Robert Crease, a historian of science and co-author of what I think is the best history of the development of the Standard Model: The Second Creation: Makers of the Revolution in Twentieth Century Physics. Crease describes Horgan as “a man who does not destroy his tapes”, and tells the following story:

I once interviewed a well known European physicist whom I had arranged to meet at a table in the noisy lunchroom at the Brookhaven National Laboratory. I pulled out a tape recorder and asked him about one of his experiments. The scientist could barely disguise his impatience. After five minutes we had a slight misunderstanding about where a certain event took place. I corrected him; he thought I hadn’t been listening.

“That’s it!” he fairly roared as he abruptly stood up, his chair shooting backwards. The background hubbub in the lunchroom suddenly plummeted and everyone turned to stare. He strode away, shouting, “This is a total waste of time! You’re an imbecile!” Or at least I think that’s what he shouted. I can’t be sure, because I destroyed the tape. I was too embarrassed to consider replaying it, or risk having others know my humiliation.

One tape I wonder if Horgan still has is that of his interview with Witten back in the mid-nineties. His chapter on string theory in The End of Science included a rather harsh portrayal of Witten, some of which I remember as being quite unfair. It’s also true that Horgan’s aggressive skepticism about the claims being made at the time for string theory has stood up very well in light of what has happened in the intervening fifteen years or so.

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The New Math

Via Steve Hsu, I ran across the cover article from Alpha magazine, a magazine for the hedge fund industry, entitled The New Math. It describes the role physicists are playing in several hedge funds, developing sophisticated trading strategies. One of the best known of the organizations doing this is Renaissance Capital run by Jim Simons, and its success is now responsible for funding the new Simons Center at Stony Brook.

Two of the theoretical physicists featured in the article were fellow graduate students at Princeton while I was there. One of them, Marek Fludzinski (who was a couple years ahead of me), quickly left academia and went on to a career in finance, ending up founding the Thales hedge fund, which he still runs. The other, John Moody (more about him here), was in my class and so I got to know him quite well, but I had lost track of him in recent years. He worked with Frank Wilczek on axions and left Princeton for Santa Barbara after Wilczek went there to the ITP.

In recent years quite a few mathematics Ph.D.s and a very large number of particle theory Ph.D.s have ended up in the finance industry, and the article describes the kinds of things that they are doing. The impact of the recent melt-down in the credit markets remains to be seen: maybe there will be fewer jobs available in this field, or maybe demand will increase for people with this kind of technical background as companies pursue ever more sophisticated strategies.

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