Not Even Wrong

When I first started studying quantum mechanics I read quite a bit about the remarkable history of the subject, especially about the brief period from 1925-27 when the subject grew dramatically out of the incoherent ideas of the old quantum theory to the full quantum mechanical formalism that is still taught today. This was the work of a small group of physicists: especially Heisenberg, Born and Jordan in Göttingen, Schrödinger in Zurich, Dirac in Cambridge, and Pauli in Hamburg. Recently I’ve been reading again about some of this history, but paying attention especially to the interactions of mathematics and physics during these years. An excellent very recent article that covers some of this is by Luisa Bonolis, entitled “From the Rise of the Group Concept to the Stormy Onset of Group Theory in the New Quantum Mechanics”. (It seems that this link is inaccessible unless you’re at a university site that has a subscription. The article should also be available at most physics research libraries as vol 27, numbers 4-5 of the 2004 issue of Rivista del Nuovo Cimento.)

I’ve written a bit about this history before, especially about the mathematician Hermann Weyl’s role, but quite a few other mathematicians were closely involved, including Hilbert, von Neumann, Emmy Noether, and van der Waerden. Much of the interaction between mathematicians and physicists took place at Göttingen, where Hilbert was the leading mathematical figure, and Weyl was sometimes a visitor, with both of them lecturing on quantum mechanics. This period was very much a high point of the interaction of mathematics and physics, interactions of a sort that were not seen again until the 1980s. Heisenberg and his collaborators learned about matrices from Hilbert and the other mathematicians at Göttingen, and Weyl was responsible for educating physicists about group representation theory and turning it into an important tool in quantum mechanics.

The Bonolis article has some amusing quotes from physicists who were having trouble absorbing what the mathematicians were telling them. Heisenberg wrote to Jordan “Now the learned Göttingen mathematicians talk so much about Hermitian matrices, but I do not even know what a matrix is,” and to Pauli “Göttingen is divided into two camps, those who, like Hilbert (or also Weyl, in a letter to Jordan), talk about the great success which has been scored by the introduction of matrix calculus into physics; the others, like Franck, who say that one will never be able to understand matrices.” Pauli was scornful about this new, unphysical, mathematical formalism of matrices, drawing a testy response from Heisenberg: “When you reproach us that we are such big donkeys that we have never produced anything new physically, it well may be true. But then, you are also an equally big jackass because you have not accomplished it either.”

Immediately after having to get used to matrices, physicists were confronted by Weyl with high-powered group representation theory, which they found even harder to understand than matrices. Famously, Pauli referred to the group theory that mathematicians were talking about as the “Gruppenpest”, but the late twenties saw a very fruitful exchange of ideas between mathematicians and physicists around this topic. Weyl’s proof of the Peter-Weyl theorem and von Neumann’s work on representation theory grew out of quantum mechanics, and the Brauer-Weyl theory of spinor representations was inspired by Dirac’s work on the Dirac equation.

It’s also interesting to note how in the years just preceding this period, much interaction between math and physics had grown out of general relativity. Noether’s work on what is now known as the Noether theorem came about because she was asked questions by Einstein and Hilbert who were trying to sort out conservation laws in GR. Weyl took up representation theory as a result of his work on the symmetries of the curvature tensor.

An amusing story I hadn’t heard before that is in the Bonolis article was one told by Edward Condon about Hilbert. He claims that when Born and Heisenberg went to Hilbert to get help with matrices, he told them that “the only times that he had ever had anything to do with matrices was when they came up as a sort of by-product of the eigenvalues of the boundary-value problem of a differential equation. So if you look for the differential equation which has these matrices you can probably do more with that. They had thought it was a goofy idea and that Hilbert did not know what he was talking about. So he was having a lot of fun pointing out to them that they could have discovered Schrödinger’s wave mechanics six months earlier if they had paid a little more attention to him.”

I’ve recently run across various interesting mathematically oriented sites, each with some connection to physics:

Alain Connes now has a web-site. He’s now a professor at Vanderbilt University as well as at the College de France. I can see him in Robert Altman’s movie “Nashville”. His site contains quite a few interesting things, including most of his research articles and some interesting survey articles about his work on non-commutative geometry. For instance, take a look at his “A View of Mathematics”, which starts off with a wonderful description of doing mathematical research and some interesting history of geometry, before surveying his recent work relating non-commutative geometry and physics.

David Ben-Zvi at Austin is organizing a new lecture series to be made available over the web called GRASP (for Geometry, Representations and Some Physics), which sounds promising although it is just getting started.

The MIT math department sponsors something called the Talbot workshops. Last year the topic was elliptic cohomology, this year geometric Langlands. Notes from the lectures are available courtesy of Megumi Harada who also maintains a useful website of geometry conferences, many of which have some sort of physics component.

Lubos Motl has taken to signing some of his postings with “leashed”, and Capitalist Imperialist Pig has speculated that “My dark suspicion is that he might have gotten caught in a PC violation in the Summers Affair, forcing him to do a T reversal to save his Lorentz invariant m ass”. Lubos wrote in to tell him “Unfortunately your intuition is perfectly correct, but I am not sure whether your imagination is big enough to imagine the scale.”

I have no idea who is responsible for the leashing of Lubos or what the reason for it is, but I figured this meant his blog would stop featuring the right-wing ideological political commentary he’s fond of. But today he has a posting about the Frist Center “filibustering” in which he says “I currently do not enjoy the freedom to tell you what I think about these things.” Actually he manages to make it pretty clear what he thinks about these things.

This leashing of Lubos is too bad, especially since I was finding myself more and more in agreement with his postings (not the ones about politics, but we seem to agree about the Landscape), and generally think the First amendment gives everyone the right to make a fool of themselves with crazed political rants if they feel like it. Lubos’s blog has also played another important role for me. Whenever people won’t believe me that string theorists can be smart and well-informed, but still crazed ideologues, all I’ve had to do is point them his way.

For the last couple days students at Princeton have been protesting the Republican’s plan to invoke the “nuclear option” and stop Democrats from filibustering a small number of Bush’s judicial nominees. This protest has taken the form of organizing a “filibuster” in front of the Frist Campus Center at Princeton, which was underwritten by Senator Bill Frist (Princeton ’74). Today Edward Witten and his wife, physicist Chiara Nappi, have joined the protest. I can’t tell what Chiara is reading from, but Ed is using a bullhorn to regale the crowd with passages from Introduction to Elementary Particles by David Griffiths.

Many thanks to my correspondent who wrote to me today to tell me about this.

Update: It seems that Josh Marshall of the Talking Points Memo weblog had something to do with this. Ed and Chiara got awarded a Privatize This! Talking Points Memo t-shirt, and there are still two more available.

According to a new article in New Scientist entitled The Theory of Everything: Are we nearly there yet? (unfortunately not available for free on-line), “The hunt for the theory of everything is turning into a road trip from hell – and don’t even ask who’s reading the map.” The article quotes Susskind and Weinberg as believing in the existence of a multiverse, even if this means that “all we can hope for from a final theory is a huge range of possibilities”.

Witten is referred to as a “string grandee”, and quoted as saying about string theory “More work has always given more possibilities – far more than anyone wanted… I hope that current discussion of the string landscape isn’t on the right track, but I have no convincing counter-arguments.” He’s welcome to my counter-arguments if he wants them: there’s not the slightest evidence for the landscape scenario pseudo-science, it’s incredibly ugly, not based on any kind of well-defined theory, explains nothing, and holds out no reasonable hope of ever explaining anything.

The article goes on to discuss the wishful thinking surrounding “M-theory”, quoting Witten as believing that M-theory may have a unique solution that fits our universe and explains the constants of the standard model. “Hope springs eternal” he says. Somebody seems to have given the writer the idea about M-theory that “theorists can prove that it exists as a mathematical construction, but they can’t actually write down its equations and there is no clear route towards doing so”, which is only true under a peculiar interpretation of the words “prove”, “exists”, and “it”. Lisa Randall is quoted as follows about M-theory: “We probably need fundamentally new principles… it’s not hopeless, but it’s going to require some deep new insight that we don’t really have.” She promotes her own work with Mukohyama on an alternate explanation of the cosmological constant.

The only person quoted in the article as thinking that there may be any problem at all with the way particle theory has been pursued for the last twenty years is Lee Smolin, who takes the absolute lack of any experimental evidence for string theory as a sign that the field may be off on the wrong track. He notes that “If you look back over the last 200 years, every decade or two there’s a dramatic advance, people always understand something new that couples theory and experiment… I suspect there is some right question that we’re not asking.”

Everyone in the particle physics community is avidly awaiting the startup of the LHC accelerator at CERN, scheduled for 2007. A new preprint by Gianotti and Mangano entitled LHC physics: the first one–two year(s) gives some idea of what to expect.

The design luminosity for the LHC is about 10³⁴cm^-2s^-1, which is about 100 times the current luminosity of the Tevatron. Current plans are to first cool down the machine in spring 2007, followed by commissioning single beams over the next few months, with first colliding beams in the second half of 2007. During 2007, most effort will be devoted to commissioning the machine, followed by a shutdown for a few months. A seven-month long physics run at luminosities of up to 2 x 10³³cm^-2s^-1 will take place during 2008. This is 20 times the current Tevatron luminosity and the Tevatron seems to be averaging a total of about 15 pb^-1 per week, so one could expect a total luminosity of up to about 10 fb^-1 to be collected during 2008. This is probably much too optimistic. Experience with the Tevatron when it was turned on at the beginning of its latest run was that for quite a while it was running at only a tenth of the hoped for luminosity. So perhaps 1 fb^-1 during 2008 is a more realistic expectation.

According to Gianotti and Mangano, 1 fb^-1 will be enough to see squarks and gluinos at masses of up to about 1.5 Tev. Seeing the Higgs is more demanding, especially if its mass is low. If its mass if above 180 Gev, it should require 5-10 fb^-1, if it is just above the LEP limit (114 Gev) it is likely to require more like 20 fb^-1.

Personally I think it’s quite unlikely the LHC will be seeing supersymmetric particles, so, of the things it is looking for, it will require good luck to get the data required to see the Higgs during 2008. Even if this does happen, I’d guess that analyzing the data would take us into 2009. If the LHC has trouble getting anywhere near design luminosity, things could take longer. Of course everyone hopes that something completely unexpected will be found. If this is dramatic enough, maybe there will be some exciting news in 2008.

This week I’m quite busy so I’m taking a break from landscape-bashing. Instead I’ll just quote someone else; it’s up to you to guess who.

“Suddenly it’s not too important whether a theory teaches us something new about the real world – either predicts new unknown phenomena or previously unknown links between the known phenomena and objects. It’s more important that such an unpredictive scenario might be true and we should all work hard to show that the scenario is plausible because we should like this scenario, for some reasons that are not clear to me.”

“The anthropic strategy is to pick as complicated Calabi-Yau manifolds as possible, to guarantee that there will be a lot of mess, confusion, and possibilities, and that no predictions will ever be obtained as long as all the physicists and their computers fit the observed Universe… This means that you don’t want to start with Calabi-Yaus whose Betti numbers are of order 3. You want to start, if one follows the 2004 paper, with something like F_{18}, a toric Fano three-fold. That’s a 3-complex-dimensional manifold that is analogous to the two-complex-dimensional del Pezzo surfaces, in a sense. But you don’t want just this simple F_{18}. You take a quadric Z in a projective space constructed from this F_{18} and its canonical bundle. OK, finally the Euler character of the four-fold X is 13,248. Great number and one can probably estimate the probability that such a construction has something to do with the real world.”

“Do we really believe that by studying the orientifold of the weighted projective space CP^{4}_{[1,1,1,6,9]}, we will find something that will assure us (and others – and maybe even Shelly Glashow) that string theory is on the right track? … If we deliberately try to paint the string-theoretical image of the real world as the most ambiguous and uncalculable one, I kind of feel that it’s not quite honest.”

“Some people used to blame string theorists that they were only looking for the keys (to the correct full theory) under the lamppost. It’s unfortunately not the case anymore: most of the search for the keys is now being done somewhere in the middle of the ocean (on the surface). Maybe, someone will eventually show that the keys can’t stay on the surface of the ocean, and we will return to the search for the keys in less insane contexts.”

This week in Santa Fe there’s the International Conference on Science and Consciousness, where Michio Kaku will be giving a keynote address. He’ll explain how “Many physicists today believe in the multiverse, i.e. Genesis is constantly taking place in a timeless ocean of Nirvana, creating Big Bangs even as you read this sentence” and will tell about experiments to confirm the multiverse theory. He’s also running a workshop at the conference on “Visualizing Higher Dimensions” in which you can learn about how to capture different planes of existence (connected by wormholes) in simple pictures. His fellow speakers include Gary Schwartz, Ph.D. who will explain how new experiments involving deceased parapsychologists and Princess Diana provide evidence for life after death, Steven Greer, M.D. who “has taken teams around the world to make contact with Extraterrestrial Lifeforms”, and a host of others. Kaku is also interviewed in this week’s New Scientist, where he explains that the Standard Model is “supremely ugly” and string theory is “gorgeous”.

This fall the Metanexus Institute, which is somehow part of the Templeton Foundation will be organizing a symposium honoring Charles Townes called Amazing Light: Visions for Discovery at which the Templeton Foundation will be announcing a “multi-million dollar, multi-year effort to catalyze research and dialogue at the boundaries of physics and cosmology” called Foundational Questions in Physics and Cosmology. Not clear exactly what this will be funding, but if you check the Templeton website you’ll find that “we do not support what might be called standard or mainstream science research”, so at least it won’t be any of that. In case you’re having trouble keeping them straight, this is real, this is a joke.

If you’re wondering how Templeton has convinced 18 Nobel Prize winners to attend, Sean Carroll has a very interesting posting explaining how he decided to pass up the \$8000 + expenses he could have made by speaking at this conference. Also if you’re wondering why Templeton gave Townes a \$1.4 million prize this year, you can read his remarks upon accepting it, where he explains that “Increasingly, science is showing how special our universe and we are, which has raised questions about whether it was indeed planned or influenced.”

In other news, Susskind seems to have ruined his chances at the \$1.4 million today. In his talk at Brown, according to Daniel Doro Ferrante he “repudiated any connections with Intelligent Design”.

Michael Dine from Santa Cruz was here at Columbia this afternoon to give a talk on “Branches of the Landscape”. His talk more or less corresponded to his recent paper with the same title. He’s following the philosophy pioneered by Michael Douglas of trying to look at the statistics of KKLT vacuum states, fixing the observed values of the cosmological constant and electro-weak breaking scales. The hope is that the distribution of supersymmetry breaking scales one gets would allow one to in some sense predict what this scale will be.

Dine finds three disconnected “branches” of the landscape, sets of vacua with different properties. The bottom line is that on two of them you have various problems getting something that looks like the real world, but you can do some kinds of counting. But on one of the branches you get lots of states with badly broken supersymmetry and the vast majority of states are in a region where there seems to be no hope to analyze what is going on. You can’t even say whether the number of these states is finite or infinite. So, he isn’t able to get the sort of prediction he and others were hoping for, but intends to keep working in this area nonetheless, with various ideas of what to try calculating. To me, he didn’t seem to have even a glimmer of a hope of ever getting even the vaguest sort of prediction out of any of this.

He did say that the landscape is now the only idea on the table for getting physics out of string theory. Brian Greene was in the audience and somewhat objected to this. Brian’s point of view appears to be the more traditional one that people should just try and cook up vacua with as many features as possible close to the Standard Model, and that once they’ve got such a thing it will have other implications for physics that can be checked. It seems to me that that kind of work has been going on for more than twenty years with no sign of success, but Brian still believes this will ultimately work out. Dine’s ideas for the future are converging somewhat with Brian’s older point of view. He seems to be giving up somewhat on the idea of counting all vacua in the Landscape, instead thinking about counting vacua satisfying some chosen conditions, e.g. being on one of his three branches. So he may be getting back to the older idea, looking at complicated constructions with some set of conditions imposed on them to make them look like the Standard Model, then hoping to extract something new, perhaps in terms of probability distributions rather than the more specific predictions people used to hope for.

Of course I find this whole thing pretty bizarre, since it’s horrifically ugly, and appears to me to have not the slightest hope of success. It’s discouraging that I don’t see any way of having a rational discussion with the people doing this. They are motivated by a hope that somehow, some way, they will find amidst this complicated mess the Standard Model, in some context that allows them to predict something else. As far as I can tell this is the purest of wishful thinking. They aren’t claiming to find anything encouraging, but they are pressing on, and convincing an increasing number of people to join them. One hopes that sooner or later they’ll get tired of this and move on to something more promising.