Not Even Wrong

• This week there’s a conference in Oxford I’d have loved to have been at. Slides from some of the talks are already posted here. The conference is in honor of Graeme Segal’s 70th birthday. Happy Birthday Graeme!
• Physics Today has a very interesting piece about the current state of HEP posted today by Burton Richter, focused on the topic of Should the US join CERN?. On the ILC, with Japan the prospective location, he takes the point of view that it’s most likely to be interesting as a Higgs factory, so a 250 GeV machine will suffice:
  

  The ongoing International Linear Collider (ILC) program is aimed at building and running a 500-GeV machine by 2020. A new ILC design study is scheduled for release in a few months, but by 2020 the LHC should have delivered enough cumulative output to make anything the ILC can produce irrelevant beyond what its lower-energy Higgs-factory option can do.

  Besides this, at the energy frontier the LHC is the only game in town, with HL-LHC and HE-LHC challenging and expensive projects that will dominate the future of the subject. If the US wants to participate, Richter argues that a new, closer formal relationship is needed. The politics here is likely to be tricky, with the US Congress not exactly keen on spending money outside the US, through an organization where the US has little influence.

  About the future he’s most worried about the too high cost of getting to higher energy permanently delivering us into the hands of multiverse mania:

  If our only theory of everything comes down to the landscape model, where we are only one of a zillion universes with the parameters we see as only a statistical accident necessary for life, the game is over. I hope not.

• One of the landscapeologists whose influence Richter is worried about is Joe Polchinski at Santa Barbara. Courtesy of the Milner prize competition, Polchinski is in line for about $3 million more influence if he beats out his two competitors next March, and UCSB has a press release about this. The press release explains that Polchinski is being rewarded for his discovery of “one of the basic building blocks of space time”
  

  According to the award citation, the Physics Frontier Prize recognizes Polchinski’s broad contributions to fundamental physics, most notably the discovery of D-branes. These have been shown to provide the atomic structure of black holes, predicted long ago by Stephen Hawking, and, as such, are one of the basic building blocks of spacetime.

  One goal of the Milner prize is to raise the profile of work that is not Nobel-worthy because it isn’t testable science, by creating a bigger prize for it than the Nobel. Unfortunately I think one side-effect of this is to blur the distinction between things we have evidence for and those that are pure speculation (with “D-branes=basic building block of spacetime” the latter, being promoted to the public as if it were the former).

• Steven Weinberg’s graduate level text on QM, Lectures on Quantum Mechanics, is now out, and I’m very much looking forward to getting a copy soon.
• The Higgs boson is Time Magazine’s Particle of the Year, Fabiola Gianotti runner up for Person of the Year.
• I recently read Benoit Mandelbrot’s posthumously published autobiography The Fractalist: Memoir of a Scientific Maverick, but don’t really have the time or interest to write a review here. Mandelbrot has an unusual life-story, starting with being hidden in war-time France to escape the Nazis.

  The thing that struck me most about the book though was that I had always assumed he was an academic outsider, but the true story is quite different. His family was academic mathematics royalty, with uncle Szolem Mandelbrojt a highly influential French mathematician at the College de France guiding him closely. A big theme of the book is Mandelbrot’s detailed explanation of the debates involved at each stage of his life over what would be his best next career move. There’s more about this than about the mathematics.

  Another reason not to write a review is that I can point to two interesting ones already out there. The Wall Street Journal got Stephen Wolfram to write one, see here, and American Scientist has one by Brian Hayes here. Hayes isn’t exactly kind to Mandelbrot, emphasizing his egotism and desire for recognition:

  Mandelbrot begins one chapter of his memoir with the declaration: “A blessing throughout life: I never wonder who I am.” He is untroubled by doubts or regrets, and untainted by false humility. In these pages you will find no self-effacing disclaimers about standing on the shoulders of giants; if Mandelbrot has seen a little farther, it is because he’s taller. From an early age his scientific hero was Johannes Kepler, and his goal in life was to accomplish something worthy of a modern Kepler, overthrowing an outworn orthodoxy. By his own account, he succeeded brilliantly, with quite a number of “Kepler moments.” (As far as I know, Kepler himself had only one.)

• For another, mathematically more interesting, discussion of a recently departed mathematician with an amazing career, see the AMS Notices article on I. M. Gelfand. Gelfand’s career and influence is a huge topic, so this is just Part I.
• A significant new advance in representation theory is explained nicely by its authors here in terms of the general philosophy of representation theory laid out by Gelfand. A standard topic in representation theory courses is to classify the unitary representations of compact semi-simple Lie groups (highest weight theory), but the question of what happens in the non-compact case is much, much more difficult and still open, with one problem that the representations are infinite-dimensional. This latest paper reports “a finite algorithm for computing the set of irreducible unitary representations of a real reductive group G” with the authors describing their result as follows”
  

  The third step in Gelfand’s program is to describe all of the irreducible
  unitary representations of G. This is the problem of “finding the unitary dual”

  G^{^}_u =_def {equiv. classes of irr. unitary representations of G}

  It is this problem for which we offer a solution (for real reductive G) in this paper. It is far from a completely satisfactory solution for Gelfand’s program; for of course what Gelfand’s program asks is that one should be able to answer interesting questions about all irreducible unitary representations. (Then these answers can be assembled into answers to the questions about the reducible representation π, and finally translated into answers to the original questions about the topological space X on which G acts.) We offer not a list of unitary representations but a method to calculate the list. To answer general questions about unitary representations in this way, one would need to study how the questions interact with our algorithm.

  All of which is to say that we may continue to write papers after this one.

  This sort of representation theory is ferociously technical, with many papers in the subject appearing to have been written only to be read by the very small number of people expert in all these technicalities. This document is surprisingly different, starting off with an accessible introduction to the subject, and then devoting a lot of space to a careful, readable exposition of the details of the necessary technicalities. The subject is still ferociously complex and technical, but this paper gives one a fighting chance to actually understand what is going on if one has the time and energy to read one’s way through it. An admirable and unusual choice of how to write a modern math paper.

Update: A commenter points out a nice article that just appeared in Scientific American, Strange and Stringy, by Subir Sachdev, who explains some recent ideas about using dualities to understand certain condensed matter phenomena.

Classes are over for the semester, and I’ve put together the lecture notes for my undergraduate “Quantum Mechanics for Mathematicians” course, which are available here.

The idea for the course was to try and explain the basics of quantum mechanics, from the point of view of unitary representations of Lie groups. While this is a rather advanced topic, I made an effort to do things quite concretely and start at the most basic level (the only prerequisite for the course was calculus and linear algebra). I hope the notes will be useful both to mathematicians trying to learn something about quantum mechanics as well as to physicists who would like to better understand the mathematics behind the way symmetry principles get used in the subject.

More to come next semester. The initial plan is to start with the fermionic oscillator, move on to path integrals, then relativity, the Dirac equation, and U(1) gauge theory (E and M), ending up with some very basic quantum field theory (non-interacting fields). We’ll see how that turns out and at what point I run out of energy and stop writing.

Any corrections, comments or suggestions about how to improve these notes are most welcome.

Update: Thanks to all for comments, I’m quite pleased to see how many people have been looking at these notes (6600 downloads and counting!). They’ve also made an appearance in surprising places, including here.

For the latest SUSY enthusiast take on the implications of what the LHC has been (not) seeing, your best bet might be yesterday’s talk at the KITP by Nima Arkani-Hamed on Naturalness. An hour and 40 minutes, no slides, nothing much on the blackboard, just him talking about how he now sees things. Some high points:

• If the Higgs turns out to have spin two, he’ll quit physics.
• If the Higgs turns out to be a techni-dilaton, he’ll kill himself.
• At this point, a natural theory would have to be rather baroque, so he favors abandoning naturalness in favor of simplicity.
• The simplest thing is the Standard Model, but that requires too much fine-tuning. He won’t completely abandon naturalness: one part in a million fine-tuning is fine, but the SM fine-tuning problem isn’t. This is the point where he loses me (going from the SM to the vastly more complicated SUSY theories with the needed SUSY breaking seems to me not close to being worth the supposed improvement in the fine-tuning).
• He complains that “Some BSM theorists are giving our field a bad name” by repeatedly making SUSY predictions that turn out to be wrong and changing their story.
• He’s not one of those: he still favors split SUSY, and has since 2004.
• Split SUSY makes a falsifiable prediction: no Higgs gamma-gamma excess. This is of course the same prediction as the Standard Model.
• In his favored version of split SUSY, all SUSY partners are much too heavy to ever be observable except the wino, bino and gluino. He had a lot to say about what observing these would tell us, but not much about what the implications are of not seeing them in the LHC 8 TeV run. Would this just mean “surely they’ll show up at 13 TeV”? Is seeing nothing at 8 TeV consistent with split SUSY? What about seeing nothing at 13 TeV?

In any case, giving up on SUSY is definitely not on the agenda as far as he’s concerned.

The New York Times is reporting that tomorrow Yuri Milner will be announcing the award of a new set of prizes for fundamental physics work, this time including some experimentalists as recipients. The awards are

• $3 million for the experimental discovery of the Higgs at CERN. This will be split into three parts: $1 million to Lynn Evans for his work building the machines, $1 million to ATLAS current and ex-spokepersons Fabiola Gianotti and Peter Jenni, and $1 million to CMS current and ex-spokepersons Joe Incandela, Michel Della Negra and Tejinder Virdee. I’m suspicious that the NYT has missed CMS ex-spokesperson Guido Tonelli, who was on the list I heard about earlier today from a source at CERN.
• $3 million to Stephen Hawking for his work on black holes.
• Three “New Horizons” prizes of $100,000 each to younger theorists working on string theory and SUSY: Niklas Beisert, Davide Gaiotto and Zohar Komargodski.
• Two “Physics Frontiers” prizes of $300,000 each to string theorists Alexander Polyakov and Joe Polchinski, with a third $300,000 prize going to a group of condensed matter physicists (Charles Kane, Laurens Molenkamp and Shoucheng Zhang) who work on “topological insulators” among other subjects.

Polyakov, Polchinski and the group of condensed matter physicists are now the contenders for the $3 million 2013 Fundamental Physics Prize which the NYT story says will be awarded “by a vote of the judges on the morning of March 20 at CERN and announced in a ceremony that evening.”

The special award to the LHC physicists should help make up for the problem that no Nobel prize may end up going to the Higgs discovery because too many people were involved. Milner has the advantage of not being bound by long tradition and arguably out of date rules the way the Nobel Committee is.

On the theory side though, these awards make it clear that the Fundamental Physics Prize story is likely to be heavily dominated by awards from string theorists to string theorists for work on string theory. Besides Hawking, all the recipients have some connection to string theory, with the condensed matter physicists working on a hot topic which many string theorists see as the future of their subject. For more about the recent history of the string theory/condensed matter connection, see this article from last year in Nature which includes this, which refers to certain books published in 2006:

“It’s hard to say whether the interest in condensed-matter applications is a direct response to those books because that’s really a psychological question,” says Joseph Polchinski, a string theorist at the Kavli Institute for Theoretical Physics in Santa Barbara. “But certainly string theorists started to long for some connection to reality.”

Update: The NYT article has been revised to include Tonelli.

Update: The press release with more details is here. There’s a story at the Guardian here. CERN has more here, including interviews with the LHC winners. They comment on the fact that they are getting awards that belong to much larger groups, with Incandela and Gianotti saying they are trying to find a way to distribute the money to younger members of the collaboration who most need it. Lyn Evans comments

I will not be driving around CERN in a Ferrari. That would be very bad for my image.

The Guardian has Hawking saying his plans for the money include helping his daughter who has an autistic son, and maybe a new vacation home.

About the question of what the previous Milner prize recipients are doing with their $3 million, I’ve heard rumors that the one mathematician, Kontsevich, has been giving it away to others. From the physics side, the only thing I’ve seen was that Witten planned to give some to J Street, a group working for peace in the Middle East.

Update: For commentary on whether ATLAS and CMS spokespersons should keep the money, see Tommaso Dorigo.

The journal Foundations of Physics has been promising a special issue on “Forty Years of String Theory: Reflecting on the Foundations” for quite a while now, with a contribution first appearing back when it really was 40 years since the beginnings (more like 43 now). The final contribution has now appeared, an introductory essay by the editors (’t Hooft, Erik Verlinde, Sebastian de Haro and Dennis Dieks).

The overall tone of the collection is one of defensive promotion of the subject. The fact that string theory’s massively overhyped claims to give a unified theory of particle physics have led to miserable failure is mostly completely ignored. From the introductory essay one would never guess that string theory was ever supposed to have something to do with explaining the Standard Model of particle physics and that there were hopes that it would find some sort of vindication at the LHC, perhaps via the discovery of SUSY (the LHC is not even mentioned in this essay). String theory is presented purely as a theory of quantum gravity that has led to new insights in mathematics and had various other applications through the dualities it has uncovered. It’s main shortcoming is described as

the lack of directly testable experimental predictions that would signal ‘string physics’

which seems to me intentionally misleading, implying that string theory makes indirectly testable predictions. The problem with string theory is that it makes no predictions about anything, not that it only makes indirectly testable ones.

Three of the eleven articles in the collection are described as representing critics of string theory. The first, from Carlo Rovelli, does do a good job of explaining many of the problems of string theory. Lee Smolin’s contribution is not much about string theory, but more an examination of the general issue of the “Landscape problem”, comparing a range of different theories in which the laws of physics are different outside our observable universe.

’t Hooft’s On the Foundations of Superstring theory calls for more attention to the lack of any fundamental description that tells us what string theory really “is”, taking the point of view:

we conjecture that the “true theory” is something totally different from superstring theory (and certainly also different from gravitating quantum field theories), but that string theory may approximate the truth to various degrees of accuracy in one or several of its compactified realizations, just as it does for some condensed matter systems and QCD.

He ends with an argument (which he notes is “one where only few readers will follow me”) that one problem with string theory is that it uses the conventional quantum formalism, which he feels is flawed, needing replacement by an “emergent” version of quantum mechanics. For more about the sort of thing he has in mind, see here.

Two articles by philosophers of science, Dean Rickles and Richard Dawid address the question of how to evaluate a supposedly scientific theory that, like string theory, makes no experimentally testable predictions. Both pieces seem to me to suffer from a rather uncritical attitude towards various forms of string theory hype. For Rickles, the dominance of string theory can be justified by its “mathematical fertility”, for Dawid the justification is “the assessment of scientific underdetermination” (roughly, there aren’t any other good ideas). That it has led to some interesting mathematics and that there’s not a lot of good alternative ideas out there are perhaps the two best arguments for pursuing string theory, but in both cases the situation is far more complicated than string theory advocates would have one believe.

The articles by string theorists (Balasubramanian, Giddings, Gubser. Martinec, Susskind and Duff) have a range of interesting things to say, sometimes amidst large dollops of string theory hype. Almost all evade serious discussion of string theory’s failure to say anything about the Standard Model (although Susskind argues, a la Multiverse, that this a positive feature of string theory). Giddings perhaps makes the most serious criticism of string theory in the entire volume, discussing its problems as a theory of quantum gravity, where other authors see a big success and the theory’s main selling point.

The article by Duff is by far the most bizarre thing in the volume, and I wrote about it extensively a year ago here. As Duff sees it, the problem is just that critics of string theory are misguided and misinformed. He includes a three page denunciation of Garrett Lisi which has nothing to do with string theory, characterizes the major recent research directions in string theory as fluid mechanics and the black hole/qubit correspondence, and has an appendix about the press release Imperial College put out making absurd claims that he had finally figured out how to make predictions from string theory (see here). The editors of the volume seem to be rather defensive about publishing such a thing, noting

Needless to say that the opinions expressed in this paper are entirely the author’s own and that it is not our intent to spark new popular or otherwise heated discussions.

but justifying it as

we are happy to include this paper in our special issue as addressing questions that are important not only to scientists but also to the wider public, which was among our initial intents.

and ending with

We warmly recommend Duff’s very readable and playful contribution.

Nothing about Duff’s piece struck me as “playful”, but that the editors see it as some sort of joke would explain why they thought it worth publishing.

Update: Over at The Browser, Steven Gubser recommends that people should read The Elegant Universe and four string theory textbooks. Asked about the “no predictions problem”, Gubser does his best to mislead, claiming the situation is just like that with QED that Feynman got the Nobel Prize for. As for SUSY, if the LHC finds it, that’s evidence for string theory, if not, no problem. There’s the old favorite “the LHC might produce microscopic black holes”. About whether string theory makes testable predictions about the heavy ion physics the LHC is studying

String theory might predict that such and such number is one, and the experiment might say well it’s about two, but it could instead be one. That’s the kind of accuracy with which things can typically be done.