Not Even Wrong

I’ve been busy with other things, but after taking a look today at various new things related to quantum gravity, I was struck by how much things have changed sociologically in that subject over the last few years. Back in the days of the “string wars”, debates about quantum gravity were fiercely polarized. Oversimplifying and caricaturing the situation a bit, the two sides of the quantum gravity debate were:

• Those interested in loop quantum gravity as well as other more exotic attempts to reformulate the problem of quantum gravity. These people just considered pure quantum gravity and devoted a lot of effort to analyzing the deep conceptual issues that arise. They sometimes considered highly speculative hypotheses, trying out abandoning the usual basic axioms, for instance replacing fundamental axioms of quantum mechanics. Lee Smolin was an influential figure, and the Perimeter Institute a major center for this research.
• String theorists, who argued that the appearance of spin-two massless mode in the quantized string spectrum showed that string theory was the only way to understand quantum gravity. They claimed that they had a single, very specific and highly technical mathematical structure to study, which obeyed the conventional quantum theory axioms. Their efforts were devoted to specific computations in this theory, and they seemed to regard the other side of the debate as woolly thinkers, caught up in meaningless ill-defined philosophical speculation. The KITP at Santa Barbara, led by David Gross and Joe Polchinski, was a major center for this side of the debate.

These days, things have changed. If you’re at Perimeter, prominent activities include:

• This week’s conference on a very technical issue in string theory, superstring perturbation theory.
• This month’s course of lectures on Explorations in String Theory.
• The next public lecture will feature Amanda Peet promoting string theory. Peet has been one of the more ferocious partisans of the string wars. The text advertising her public talk a few years back at the Center for Inquiry in Toronto warned attendees who might consider “parrotting of critical views by outsiders like Lee Smolin.”

On the other hand, it you’re in Santa Barbara these days, you might be participating in a KITP conference on Quantum Gravity Foundations. This is featuring very little about the technical issues in superstring theory being discussed at Perimeter, but a lot of discussion of deep conceptual issues in quantum gravity. There’s also a lot of willingness to throw out standard axioms of physics, maybe even quantum mechanics. They’re even letting Carlo Rovelli talk.

The sort of speculation going on at the KITP is featured on the cover of this month’s Scientific American, and this week Quanta magazine will be publishing a series of pieces on something related, the “ER=EPR” conjecture. There’s debate whether anyone really understands this and whether it is consistent with standard quantum mechanics. It also features a diagram that people call the “octopus” diagram. Back in the day it was Lee Smolin who was getting grief for an “octopus” diagram (see here), yet another way in which things have changed.

For a more balanced view of quantum gravity issues, you might want to spend your time in France, where the IHES recently hosted an interesting series of surveys of the subject (see here), and the Quantum Gravity in Paris conference featured more specialized talks. In the category of quantum gravity topics I wish I had more time to learn about, Kirill Krasnov’s talk was presumably related to this recent work, which looks intriguing.

Cédric Villani is in town today, giving a talk at the French consulate. He’ll discuss his book, recently translated into English (I wrote a bit about it here). Yesterday, despite the lack of suitable bread and cheese, he was in Princeton, where he gave a public lecture at the IAS. The New Yorker has a story about him by Thomas Lin, entitled The Lady Gaga of French Mathematicians Comes Stateside.

If you’re not listening to Villani tonight, you could be watching a PBS Nova program on mathematics, The Great Math Mystery. Among the mathematicians interviewed will be my colleague Dusa McDuff. As for the question on the PBS site:

Is math a human invention or the discovery of the language of the universe?

the answer is the latter.

What some mathematicians might consider the “Great Math Mystery” is whether Mochizuki really has a proof of the abc conjecture. There finally will be the topic of a workshop involving experts in the field, to be held this December in Oxford. Still no paper from Go Yamashita about this, but here you can find some photographs of the boards from his talks in Kyoto last month. Mochizuki himself has a new paper, inspired by conversations with Fesenko.

Also in New York this week, Bjorn Poonen will be speaking on Thursday. His topic is a heuristic argument that there is a finite bound on the rank of elliptic curves. For notes from a talk of his about this last year, see here.

Update: The Villani IAS talk is available here.

Update: At David Mumford’s blog he has a long and very interesting posting about the state of mathematical research publishing.

Update: One more piece of math news. Dan Rockmore has set up a public version of his Concinnitas Project, which lets people post, with explanation, a picture of their choice of a “most beautiful mathematical expression”. See here for details.

The LHC has just ramped up for the first time to 6.5 TeV, and has a probe beam circulating in one direction, the highest energy protons humans have ever accelerated. You can follow what’s happening here.

The BBC has gotten very excited about this whole LHC thing.

Update: Now it’s two beams at 6.5 TeV. They just need to be careful to avoid beam collisions until the press event is organized…

Update: Maybe they weren’t careful enough. The Monday morning beam commissioning reports “Possibly first collisions”. No confirmation of this from the experiments, or officially from CERN.

Some news from all over:

• The problem with a short in the LHC seems to have been resolved (one can follow progress here), looks like they’ll be ready to inject a beam in a few days. Also looks like they’re not likely to spend their Easter Sunday doing this, so, maybe it will be next Monday?
• Cambridge has finally gotten around to choosing a new Lucasian professor (the last two were Michael Green and Stephen Hawking). Michael Cates will take the position July 1.
• Grothendieck’s death last year was sad to hear about, but a positive result is that the Grothendieck Circle is back in the business of making available resources concerning his work. There’s a comment at the top of the website that
  

  With the agreement of Grothendieck’s family, the work of the Circle to bring Grothendieck’s unique story and writings to the public has resumed.

• There was a workshop this past month devoted to Mochizuki’s work, but I haven’t found anyone who knows what happened there. Minhyong Kim has taken to trying to write about Mochizuki’s ideas on MathOverflow, see here.
• The Toronto Star has a long article about Langlands.
• At the KITP this week a new program on quantum gravity is starting. This month’s Scientific American has a Joe Polchinski cover story on Burning Rings of Fire. Maybe some of the KITP talks will be enlightening, but the small amount of time I’ve spent trying to follow the past two years of debate on this has just left me mystified, struggling to see how the very general framework people seem to be working in can possibly lead to a resolution of the questions they’re concerned with.
• Frank Wilczek has a speculative article about Physics in 100 years. A commenter here suggests comparing it to Wilczek’s version of nearly fifteen years ago. The last fifteen years have not been kind to Wilczek’s hopes for vindication of SUSY or SUSY GUTs, but he’s not giving up yet. It will be interesting to see what his reaction will be if the next fifteen years are equally discouraging.

  I do very much like one thing in the new version, the section about possible unification of ideas of quantization and of symmetry, where he speculates:

  Quantization and fundamental symmetry will not appear as separate principles, but as two aspects of a deeper unity.

  That’s pretty much one of the main motivations of the book I’m writing (see here).

Update: There are rumors going around tonight that there’s been a hoax perpetrated on the arXiv, something like the Sokal hoax. This has to do with an hep-th posting entitled Riding Gravity Away from Doomsday, which has appeared under the name of a very prominent string theorist, Ashoke Sen, winner of the $3 million Milner Fundamental Physics Prize. What I’m hearing is that no one can believe that Sen could possibly have seriously written something this silly, so it must be some sort of hoax. Speculation is that the hoax could have been carried out to make the hep-th moderators look bad, by showing that they’ll agree to anything, no matter how absurd, if it invokes the Landscape and the multiverse. Some think that Sen’s account must have been hacked and then used to post the nonsense paper, others think that Sen himself is behind the hoax, having had enough of the Landscape business. I’ll update this as more information becomes available.

Update: At least some papers on the arXiv still are serious.

Update: Beams are back in the LHC, successfully circulated at 450 GeV on Easter Sunday (live blog here). Next step, ramp up to 6.5 TeV.

I’m heading off soon on spring break, planning on traveling to Scandinavia and hoping to see a solar eclipse. There hasn’t been much news recently from the math and physics worlds, and it’s unlikely I’ll be blogging until I get back (around the 24th), so will turn off comments while away.

I hadn’t thought until recently about the fact that this year is the 100th anniversary of Einstein’s discovery of the field equations of general relativity, so there will be quite a few events taking place commemorating this (for a list of some, see here). This week’s Science magazine has a special issue on the topic. It includes news stories about LIGO and gravitational waves, new tests of the equivalence principle, and possible tests of GR from observations of the black hole at the center of our galaxy.

There’s also a review of a book from a few years ago about Einstein’s search for a unified theory, Einstein’s Unification by Jeroen van Dongen. The review addresses something I mentioned in my recent essay about mathematics and physics, that the development of GR provides a good example of a successful theory coming out of not just experiment and “physical intuition”, but motivated also by the serious use of deep mathematical ideas. According to the review:

Einstein employed two strategies in this search [for the GR field equations]: either starting from a mathematically attractive candidate and then checking the physics or starting from a physically sensible candidate and then checking the mathematics. Although Einstein scholars disagree about which of these two strategies brought the decisive breakthrough of November 1915, they all acknowledge that both played an essential role in the work leading up to it. In hindsight, however, Einstein maintained that his success with general relativity had been due solely to the mathematical strategy. It is no coincidence that this is the approach he adopted in his search for a unified field theory.

Besides the fact that Einstein said so, other evidence for the primacy of the mathematical strategy in this case is the simultaneously successful work by mathematician David Hilbert, who was definitely pursuing the mathematical strategy.

While I think there’s an excellent argument that a mathematical approach was crucial in Einstein’s discovery of the field equations, the later history this book deals with also shows the dangers this can lead to. Einstein spent much of the rest of his life on a fruitless attempt to get a unified theory by pursuing the same mathematics he had so much success with in the case of GR. It’s a good idea to keep in mind both examples. On the one hand, trying out some new deep mathematical ideas can lead to success, on a time scale of a few years. On the other, if you’ve spent 30 years pursuing a mathematical framework that has gone nowhere, maybe you should do something else. A lesson that Einstein’s successors at the IAS might want to keep in mind…

The story about new tests of the equivalence principle contains the usual nonsense about testing “string theory predictions”:

Using beryllium and titanium, they found gravitational and inertial mass equal to one part in 10 trillion, as they reported in Physical Review Letters in 2008. That’s not quite precise enough to test string theory predictions.

That “string theory predicts violations of the equivalence principle” is what used to be called a “factoid”, something not true repeated so often that it becomes a fact. It seems though that usage has changed, with “factoid” now often being used to refer to something true. A new word is needed.

Update: See here for an article by Michel Janssen and Jurgen Renn discussing in detail the question of the “mathematical” versus “physical” strategies in Einstein’s discovery of the GR field equations.

• The LHC is getting close to the point where it can be restarted with a 6.5 TeV beam energy. Latest news here, schedule here. Plan is for a sector test late next week (beam in part of the machine), beam in the whole machine March 23. First physics run May 18th.
• Next week there will be a conference in Venice devoted to neutrinos, blogging going on here.
• There may be some progress on the Mochizuki/abc front. Ivan Fesenko has written up some notes that try and put Mochizuki’s ideas in context with some other more conventional parts of mathematics. The week after next will see a workshop in Kyoto, with lectures from Go Yamashita on the abc proof. Another recent survey talk by Mochizuki is here.
• The latest AMS Notices has a series of articles about the life and work of Arthur Wightman, one of the main figures in the effort to make rigorous sense of quantum field theory.
• In my essay about math and physics, I mentioned the Atiyah-Bott work on the moduli space of solutions to the Yang-Mills equation in the case of Riemann surfaces. This has an intriguing analog to the function field case, which was discussed already by Atiyah and Bott. Dennis Gaitsgory has a new paper out that touches on this in the context of his proof (with Jacob Lurie) of the Weil Tamagawa number 1 conjecture for function fields (see here). The new paper has the footnote: “The contents of this paper are joint work with J. Lurie, who chose not to sign it as author.”
• Returning to physics, Princeton University Press announced that Frank Wilczek will edit a Princeton Companion to Physics, modeled on the wonderful Princeton Companion to Mathematics, which was edited by Tim Gowers. Publication is planned for 2018.
• Caltech hosted a workshop the past couple days, inaugurating the Walter Burke Institute for Theoretical Physics. Hopefully they’re well-funded enough to put videos or slides online. John Preskill’s remarks at a celebration of the event are available here. He gives some principles for doing science that I very much agree with. In recent years I’ve become especially aware of the importance of his first principle: “We learn by teaching”, since I’ve been learning a lot that way. As the trend grows towards institutes modeled on the IAS and prestigious positions that involve no teaching, I think this needs to be kept in mind.

  I also agree with his last principle: “Nature is subtle”, and found very interesting his comments on the holographic principle:

  Perhaps there is no greater illustration of Nature’s subtlety than what we call the holographic principle. This principle says that, in a sense, all the information that is stored in this room, or any room, is really encoded entirely and with perfect accuracy on the boundary of the room, on its walls, ceiling and floor. Things just don’t seem that way, and if we underestimate the subtlety of Nature we’ll conclude that it can’t possibly be true. But unless our current ideas about the quantum theory of gravity are on the wrong track, it really is true. It’s just that the holographic encoding of information on the boundary of the room is extremely complex and we don’t really understand in detail how to decode it. At least not yet.

  This holographic principle, arguably the deepest idea about physics to emerge in my lifetime, is still mysterious. How can we make progress toward understanding it well enough to explain it to freshmen?

  From what I can tell, the problem is not that it can’t be explained to freshmen, but that it can’t be explained precisely to anyone, since it is very poorly understood. The AdS/CFT conjecture is now older than some of my current students, with a literature of more than 10,000 papers, but taking a look recently (see here) at what should be a toy model case (AdS3/CFT2) reminded me just how little seems to be truly understood. This is a quite odd and I think historically unprecedented situation.

• Somewhat related to the holography question, for anyone interested in condensed matter physics, I recommend taking a look at Ross McKenzie’s blog Condensed Concepts. He discusses some of the issues related to attempts to use holography in condensed matter. He also has a recent paper (with Nandan Pakhira) showing a violation of a bound suggested by holographic arguments.

Update: On the multiverse mania front, tomorrow Science Friday is hosting Sean Carroll to continue his war against falsifiability and the conventional understanding of science, joined by Seth Lloyd to help promote the multiverse. Perhaps it should be “Pseudo-science Friday”?

Update: Michael Harris’s book now has a blog, which promises to discuss topics that didn’t make it into the book.

Update (March 7): Beam is back in the LHC (well, at least in a part of it). There was a successful test today, sending beam into one sector in one direction, two in the other, see here.