The semester here is finally underway, and I’m getting back to work on my quantum mechanics and mathematics book (latest version available here). Current plan is to have a final version by next spring, with publication by Springer late next year. This semester I’m teaching Calculus II, a subject where there’s only one thing I really dislike about pretty much all textbooks, their refusal to use Euler’s formula. Since I couldn’t find an online source I was completely happy with, I spent some of the last couple days writing up some notes for the students on Euler’s Formula and Trigonometry, which maybe someone else will find useful. In other news:
- Nima Arkani-Hamed was here today, giving a talk on a new model he calls “NNaturalness”. The basic idea is to consider something like N copies of the Standard Model, with N a large number. Large N fixes the technical naturalness problem, with something like N=104 fixing the MSSM’s current naturalness problem, and N=1016 fixing the non-supersymmetric problem. He makes clear that he’s well aware that this is a pretty contrived thing to do, but argues that it’s interesting one can do this while evading dramatic disagreement with experiment, and coming up with potential CMB signatures soon observable (e.g. the effective number of relativistic degrees of freedom).
He has a nice description of the naturalness problem as “in any theory where we can compute the mass of the Higgs it has a fine-tuning problem”. Probably there are people out there who think they have a way to compute the Higgs mass who would disagree with him. To me the problem is that the theories he’s talking about (GUTs, string landscape) don’t actually explain anything about the underlying physics of electroweak symmetry breaking (where does the Higgs field come from and why does it have those couplings?). Given this, it’s unclear why one should worry about the fine-tuning.
He describes the landscape and the multiverse as “like democracy, the worst idea except for everything else”, and gives a defensive argument for why one should study alternatives like “NNaturalness”, even if they’re not as good as the multiverse (which he finds “simple and deep”). To him it’s worth thinking about alternatives to the multiverse (as a “foil”) not because the multiverse is untestable pseudo-science, but because maybe one shouldn’t just give up. So, it seems that at this point he’s not quite signing up with the intellectual suicide of multiverse mania, although he sees it as the most attractive path available.
In other Arkani-Hamed news, the IAS has an article about his activities promoting a next generation collider here.
- The KITP has a newsletter here, including a description by Graham Farmelo of his visit there. Oddly, no matter what he writes about, Farmelo almost always includes an unconvincing defense of string theory and/or the current activities of string theorists (for examples, see here, here, here and here). In this case he assures us that the KITP theorists are not given to “mathematical adventurism”. I think he’s right, but that’s the problem…
- Someone pointed me recently to Olivia Caramello’s web-page on Unifying theory and her arguments with fellow category theorists. I had a youthful infatuation with category theory, but ultimately came to the conclusion that there’s a real danger in that kind of “unification” of going too far in the direction of saying less and less about more and more. Many of the ideas involved are powerful and attractive, but the remarkable thing about mathematics is that, even for the lover of grand ideas, less generality is sometimes even more so.
Update: One more. If you’re in the Bay Area next week, you might want to head up to MSRI for a series of elementary talks on the Langlands program by Edward Frenkel.