Not Even Wrong

I recently mentioned that funding for the RSVP experiment is being reevaluated. More details about this are available in a recent issue of Science magazine.

The Rare Symmetry Violating Processes (RSVP) project is a proposed experiment at Brookhaven that would have two components. One, “MECO” would search for neutrinoless conversion of a muon to an electron, observation of which would indicate new physics beyond the standard model. The other component, “KOPIO”, would try and measure the decay rate for neutral kaons to a pion, neutrino and anti-neutrino, a CP violating decay whose rate is predicted by the standard model.

Last fall the NSF had allocated money to start building the experiment, which was projected to cost $158 million. The idea was to use the AGS accelerator at Brookhaven, which in recent years has mainly been used as an injector for the heavy-ion collider RHIC. It seems though that revamping the AGS for use by RSVP may cost a lot more than people had originally thought, pushing the cost of RSVP up to as much as $300 million. The potential cost of RSVP is being reviewed, and HEPAP has been asked to evaluate the results that RSVP may be able to achieve at different levels of funding. According to Michael Turner, head of mathematical and physical sciences at the NSF, “We will reevaluate [RSVP’s] scientific value, its cost, and then make a decision.”

The SPIRES database is used each year to produce a list of the most frequently cited papers in particle physics. This year’s list has appeared, although the usual annual discussion of the list from Michael Peskin still hasn’t yet. The trends I commented on last year in the 2003 list are even more pronounced this year.

The top ten most highly-cited papers in particle physics are now dominated by experimental results in astrophysics and cosmology with five papers in this category. Particle theory is represented by three large extra dimension papers from 1998 and 1999, and a single string theory paper, Maldacena’s 1997 article on AdS/CFT. The Maldacena paper is now the fourth most highly cited particle physics paper of all time, surpassed only by citations of the Review of Particle Properties, Weinberg’s 1967 paper, and the 1973 Kobayashi-Maskawa paper.

Even more so than last year, this data shows that particle theory and string theory flat-lined around 1999, with a historically unprecedented lack of much in the way of new ideas ever since. Among the top 50 papers, the only particle theory ones written since 1999 are a paper about pentaquarks by Jaffe and Wilczek from 2003 at number 20, the KKLT flux vacua paper at number 29 and a 2002 paper on pp waves at number 32.

How many more years of this will it take before leaders of the particle theory community are willing to publicly admit that there’s a problem and start a diiscussion about what can be done about it?

For some other interesting statistical data gathered from this database, check out the SPIRES playground.

One relatively recent idea that probably hasn’t fully shown up yet in the yearly citation counts is Witten’s late 2003 idea about relating gauge theory and the topological string in twistor space. While the idea of working in twistor space has lead to a lot new results about gauge theory amplitudes, Witten’s original hope of relating gauge theory and string theory seems to be in trouble.

There’s a quite interesting discussion going on about Wick rotation over at Lubos Motl’s weblog.

In flat space-time, the situation is well-understood: if your Hamiltonian has good positivity properties you can analytically continue to imaginary values of time, and when you do this you end up with “Euclidean” path integrals, which actually make sense, unlike QFT path integrals expressed on Minkowski space, which don’t. You can see the problem even in free field theory: the propagator is given by an integral that goes through two poles, so is ill-defined. The correct way to define it to get causal propagation for a theory with positive energies is to go above one pole, below the other, which is equivalent to “Wick rotating” the integration contour 90 degrees to lie on the imaginary time axis.

In a curved space time, things are much trickier. And in a path integral approach to quantum gravity it is very tricky. Do you integrate over all metrics with Lorentz signature (ignoring the fact that the path integral doesn’t really make sense for a single one), or do you integrate over Euclidean signature metrics (Euclidean Quantum Gravity)? There are arguments against either choice, not to mention the non-renormalizability problems that both may have. For some of the arguments, see the debate in Lubos’s comment section, which gives some idea of how confused the state of this question is. Another good reference is the article by Gary Gibbons in the Hawking 60th birthday celebration volume. It doesn’t seem to be on-line, but his talk at the workshop is.

I’ve always thought this whole confusion is an important clue that there is something about the relation of QFT and geometry that we don’t understand. Things are even more confusing than just worrying about Minkowski vs. Euclidean metrics. To define spinors, we need not just a metric, but a spin connection. In Minkowski space this is a connection on a Spin(3,1)=SL(2,C) bundle, in Euclidean space on a Spin(4)=SU(2)xSU(2) bundle, and these are quite different things, with associated spinor fields with quite different properties. So the whole “Wick Rotation” question is very confusing even in flat space-time when one is dealing with spinors.

Over the years I’ve tried to sell the outrageous idea that one should define QFT in Euclidean space time, with one of the two SU(2)s in Spin(4) being Spin(3), the spatial rotations, the other being the SU(2) of the electroweak gauge group. I’ve never been able to get anyone to take this seriously, partly because I’ve never come up with a well-defined way of writing down path integrals which implement this idea.

There’s a story in this Sunday’s New York Times television section describing how Ed Witten pitched a story idea to the people who make the new TV show Numb3rs. According to one of the show’s executive producers, Cheryl Heuton, “Ed sent our script back along with an episode idea, which we used, telling us we should do something about a rogue mathematician who tried to crack Internet security by solving the Riemann hypothesis.” Witten had received the Numb3rs script to look at from his brother, the writer Matt Witten.

For more about the Caltech mathematicians who are the main consultants for the TV show, see this USA Today article.

Last night ABC News ran a two-hour primetime special on The UFO Phenomenon — Seeing is Believing. As part of this special program, they interviewed “one of the world’s leading theoretical physicists”, who, according to Bob Park, “looked a lot like Michio Kaku.” This physicist told ABC that UFOs should be taken seriously since “You simply cannot dismiss the possibility that some of these UFO sightings are actually sightings from some object created by … a civilization perhaps millions of years ahead of us in technology.” He also explained how aliens could get here using wormholes.

Kaku appeared yesterday on the radio show “Coast to Coast” to discuss UFOs and the ABC special. He appeared on the same show (in different hours) as Al Bielek, who evidently had a job in California, but regularly traveled by secret underground subway to Montauk, Long Island to work on the “Montauk Project”. During the 1980s he traveled to Mars on several occasions, as well as to “a research station in 100,000 BC, other planets to get canisters filled with Light and Dark Energy, and to the year 6037.”

I recently acquired a copy of the new volume 6 of Atiyah’s collected works, which contains things he wrote from the late eighties until very recently (the latest article is his joint paper with Graeme Segal on twisted K-theory). Unfortunately the price of this book is very high (about $200). I’ve bought cars for less than what I paid for the book.

Even more expensive is the full six-volume set, which Oxford intends to sell for $1000. Luckily I bought the previous 5 volumes quite a few years ago at a somewhat more modest price. Atiyah is one of my great heroes among mathematicians. He’s up there among the top very few in any reasonable list of the greatest mathematicians of the second half of the twentieth century, and the extent of his influence in bringing together mathematics and physics is hard to overestimate. Witten’s great work on topological quantum field theory was done very much because of impetus from Atiyah. One of the articles in the new volume is the write-up of Atiyah’s amazing talk at the Weyl Symposium in 1987, where he first suggested that there should be a four-dimensional QFT whose observables were Donaldson invariants and whose Hilbert space was Floer homology.

Atiyah is also known as Sir Michael. Before I heard about this I had always thought that the British system of honorary knighthoods was pretty silly, but the fact that they chose him gave me some respect for the whole system.

It’s a shame the books are so expensive, since they are wonderful documents that deserve wide distribution. Atiyah has not only discovered wonderful new mathematics, but he writes about it in an elegant, inspiring and lucid way. The books contain many expository pieces he has written over the course of his career, and these are pretty much all well worth reading. I regard a large part of my mathematical education as having come from spending a lot of time with these volumes over the years.

In a Stanford University press release today, Susskind promotes the “Landscape”, calling each different vacuum state a “pocket universe”. Referring to people like David Gross who oppose the idea, Susskind says: “More and more as time goes on, the opponents of the idea admit that they are simply in a state of depression and desperation”.

I’m wondering exactly which string theorists have admitted to him their depression and desperation.

It seems that Susskind’s new book coming out in a couple months isn’t about the Landscape, but rather black holes and holography. He’s writing another one now, to be called “The Cosmic Landscape”.

In other news, Witten will be giving a Distinguished Lecture Series in April at the Fields Institute in Toronto as part of their year-long program on the geometry of string theory. Witten seems to have decided that there’s not much to say about string theory these days, since the topics of his talks are listed as “Relativistic Scattering Theory”, “Gauge Symmetry Breaking”, and “The Quantum Hall Effect”.

By far the most important event for particle physics during the next few years will be the beginning of operation of the LHC, now planned for 2007. Besides that, here are various sources of information about what else will be going on, especially in the U.S.:

A National Research Council committee called EPP 2010: Elementary Particle Physics in the 21st Century was formed last year, charged to:

“Identify, articulate, and prioritize the scientific questions and opportunities that define elementary-particle physics.”

and

“Recommend a 15-year implementation plan with realistic, ordered priorities to realize these opportunities.”

It has already had a couple meetings, and presentations to these meetings are available here. They plan to have more public meetings this year and produce a report by the end of the year.

If you want to follow the details of current and future funding for particle physics in the U.S., there’s a lot of information in the presentations to this week’s HEPAP meeting. The overall picture is for particle physics funding to decrease over the next few years, under the pressure of the huge U.S. budget deficits. Beyond a proposed 3.1% cut for particle physics next year, the DOE is planning for another 3.7% cut in its overall science budget over the following five years. In this environment it is very difficult to find funding for new projects. One proposed new one, called BTeV, which was to study B-physics at the Tevatron, is slated for cancellation. Another, RSVP, a search for rare decays at Brookhaven, is being reevaluated.

The DOE budget document points out that the future of Fermilab is a problematic issue. Tevatron operations are slated to wind down in FY 2009, when the LHC should start producing data. The new NuMI/MINOS neutrino beam and detectors will still be running then, but it is not clear for how long. Unless a major new machine (such as the ILC linear collider) is sited at Fermilab, it’s not clear what the laboratory will be doing after 2010. Such a major new machine would be expensive, so it’s not something that could be financed out of a DOE HEP budget that continues to decline. There’s a comment about this in Jochen Weller’s weblog.

There’s a conference this week in Aspen on The Highest Energy Physics and some of the talks are already on-line.

Finally, Serkan Cabi at MIT has put together a nice collection of links to videos of physics seminars, he also has a weblog.

The great French mathematician André Weil spent the months of February-May 1940 in a prison in Rouen, as a result of what he referred to as “a disagreement with the French authorities on the subject of my military obligations”. Others might have called this “draft evasion”, and the story has something to do with why one of the most famous French mathematicians spent his post-war career not in France, but in Chicago and Princeton.

Weil’s sister was Simone Weil, who could variously be described as a moral, political and religious philosopher, an activist and mystic. She died in 1943 in England, from some combination of tuberculosis and starving herself out of sympathy with her compatriots in occupied France. During her brother’s prison stay they exchanged letters which were later published. One of these letters is a remarkable mathematical document that André Weil wrote to his sister, although she would have had little chance of understanding what he was talking about. It is reproduced in his collected works, and an English translation has just appeared in the latest Notices of the AMS.

The focus of Weil’s letter is the analogy between number fields and the field of algebraic functions of a complex variable. He describes his ideas about studying this analogy using a third, intermediate subject, that of function fields over a finite field, which he thinks of as a “bridge” or “Rosetta stone”. For function fields over a finite field, the analogies with number fields are quite close and many facts one knows about one subject can be used to make conjectures about what is true for the other. Some examples include the Riemann-Roch theorem and the Riemann hypothesis. After getting out of prison and leaving for the U.S., in 1941 Weil was able to prove the Riemann hypothesis for the function field case; of course for the number field case it remains an open problem.

For much more detail about this analogy, there’s an interesting textbook by Dino Lorenzini called An Invitation to Arithmetic Geometry.