Someone wrote in to inform me that Alain Connes has made available at his web-site the full text of his long 1994 book Noncommutative Geometry. This is a rather amazing book, in many ways more of a research document than a purely expository work. All sorts of interesting things in it, mainly about Connes’s ideas linking the “geometry” of non-commutative “spaces” and the theory of operator algebras, much of this via K-theory.
Last week there was a conference on this topic at Vanderbilt. Connes gave talks there focusing on his recent work related to renormalization. Another main topic of the conference was zeta-functions, and recent developments related to Connes’s program for understanding more about them (and perhaps proving the Riemann hypothesis) using ideas from operator algebras and non-commutative geometry. The series of lectures by Consani provide a good introduction to modern ideas about zeta functions and motives that underly this program.
The CERN Council Strategy Group has produced two very interesting “Briefing Books” for its study of strategy for the future of particle physics in Europe.
For something kind of hilarious, see a paper from 2000 pointed out by one of the commenters here. It’s by Gordon Kane, Malcolm Perry and Anna Zytkow and entitled The Beginning of the End of the Anthropic Principle. The authors tell us that in string theory, “in principle, and eventually in practice, all of the masses are calculable, including the up and down quark masses, and the electron mass. There is not any room for anthropic variation of the masses in a string theory.” The opposite conclusion now seems to dominate string theory research, with the paper many people reference as launching the anthropic landscape that of Bousso-Polchinski written a few weeks after Kane et. al. (although Schellekens and no doubt others would claim that they had the idea much earlier).
David Gross recently gave a series of lectures at Princeton entitled “The Search for a Theory of Fundamental Reality” and they are available on-line. When introducing Gross, Curt Callan noted that Princeton University Press hopes that he’ll turn his lectures into a book that they would publish. The last lecture concerns the problems and prospects of string theory and is very similar to one commented on here a couple years ago in the first real posting on this weblog. Gross says about string theory “so far, we haven’t really calculated anything”, and goes on to give three reasons for this:
1. More and more possible compactifications have been found, all of which seem to be equally consistent.
2. Don’t understand how to handle broken supersymmetry.
3. The cosmological constant problem.
The reasons he gives for continued optimism about string theory unification despite these problems are that “we still don’t know what string theory really is”, and there is no consistent picture of cosmology that is understood within the string theory framework.
He explains the anthropic landscape scenario and how it destroys predictivity, then says that some of his colleagues have given up on Einstein’s dream of finding a unique theory with no adjustable parameters, but that he himself won’t do so until he is forced to, and he isn’t forced to yet since we don’t know what string theory is. He made his usual speculation about string theory leading to some still unknown new emergent view of space and maybe time, then went on to give three reasons for supporting continued research in the subject despite its failure to make any progress on its main problems:
1. String theory has given new insights into gauge theory and maybe it will help solve QCD.
2. String theory has given new insights into mathematics.
3. String theory has lead to new speculative phenomenological scenarios (braneworlds).
About point 3. he describes the possibility of evidence for such scenarios showing up at the LHC as “very unlikely” and even says that he is willing to take bets with anyone for any amount of money that the LHC will not see such things (perhaps he should have discussed this with the authors of the recent report that used these scenarios to try and sell the ILC…). I’ve seen this phenomenon before, but it seems to me peculiar to give as a positive argument for string theory that it leads to the study of phenomenological scenarios that you don’t believe.
After his talk, a questioner asked him if string theory might turn out to just be unsuccessful (i.e. wrong), to which Gross responded “String theory can’t be wrong (or even killed)”. He elaborated by saying that it couldn’t be wrong because it was related via AdS/CFT to N=4 supersymmetric Yang-Mills, which was in turn was related to the standard model. Somehow he felt this was an argument that string theory couldn’t be wrong, only incomplete. He acknowledged that recently he had come to the point of view that string theory was not something that led to unique predictions about the world, but that it is incomplete. In this view, string theory is just a framework, like QFT, and some new ideas need to be added to it to turn it into something that really relates to the real world.
Someone asked him about LQG, and he responded by saying that he doesn’t usually comment on LQG in a polite audience, that it wasn’t very successful, didn’t connect to GR, and was not of any interest to physics.
He ended with some pessimistic comments about the possibility that the scientific community might lose the will to go on at some point in the future as it became more and more difficult to get information about shorter and shorter distance scales, or moments closer and closer to the big bang.
Update: There’s an article entitled Hard Landscape by J.R. Minkel in the June 2006 Scientific American. It deals with the Denef-Douglas work showing that finding a vacuum in the landscape with sufficiently small CC is likely to be a computationally intractable NP hard problem.
“The Douglas-Denef paper is surely a problem for drawing conclusions about what the landscape predicts,” asserts Thomas Banks of U.C. Santa Cruz.
Update: Besides the well-known Theoretical Particle Physics Jobs Rumor Mill which deals with tenure-track hiring, there’s now the Theoretical Particle Physics Postdoc Jobs Rumor Mill, which deals with postdocs. This year I count among the postdoc hires 31 string theorists, 12 phenomenologists and 5 hard to characterize, with several major institutions that hire multiple post-docs still only hiring string theorists. The rumors I’ve been hearing that only phenomenologists are getting jobs seem to be complete bunk.
Update: heppostdoc points out that the Postdoc Jobs Rumor Mill is very new and the data is incomplete. Probably complete data would show postdoc hires not as heavily weighted towards string theory.
Update: There’s a conference going on near Washington this week entitled From Quantum to Cosmos: Fundamental Physics Research in Space. Mark Trodden is blogging from the conference over at Cosmic Variance.
Update: Eric Weinstein, who continues to conduct his research in mathematics and physics from within the financial industry here in New York, will be giving a talk at the Perimeter Institute on Wednesday at 2pm, with the title “Gauge Theory of Economics”. Here’s his abstract:
The close relationship between geometry and fundamental physics can be seen from surveying the basic equations underlying the known forces of nature. What has made these repeated appearances of gauge fields and curvature tensors particularly striking in recent years is lack of any comparable applications outside of the Standard Model and General Relativity. In this talk we will pose the question of whether Yang-Mills theory is simply a unifying principle with application well beyond its current use by exhibiting unreasonably effective applications of Gauge Theory beyond those familiar in the Natural Sciences. Armed with these examples, we will then revisit the question about what is most truly special about the Standard Model and Relativity.