Various things that I’ve been wanting to mention:
Steven Hawking has a paper out, on his version of the Landscape story, using amplitudes that don’t rely upon string theory or eternal inflation. But just like the string theory Landscape I don’t see how his proposal is testable. It completely gives up on saying anything about particle physics, even statistically
If the volume weighted amplitude for the standard model vacuum is non-zero, it is irrelevant what the volume weighted amplitudes for other vacuum states are. The theory can not predict a unique vacuum state. Instead we have to input that we live in the standard model vacuum.
He ends with
The amplitudes will be highest for states in which the whole universe is in a single state, rather than a mosaic of different states, as predicted by eternal inflation. There will be no primordial production of topological defects, such as monopoles, and cosmic strings. Not all states in the landscape will have significant amplitudes, but there will be more than one that do, so M theory does not predict a unique low energy particle physics theory. It is implausible that life is possible only in one of these states, so we might have chosen a better location.
John Baez has a new This Week’s Finds out, with interesting discussions of the topos-theoretic approach to quantum theory, and the analogy between the integers and three-dimensional space. This semester he is running a seminar on “Geometric Representation Theory” (not clear how close this is to the use of the term by those representation theorists who work with D-modules). Videos and lecture notes from the talks are available, along with some blog postings (see here and here).
As always, Terry Tao’s blog has wonderful postings and articles, often of a general expository nature. For some recent examples, see one about the Schrodinger Equation, and another about Jordan normal form.
Besides excellent expository physics postings such as the recent one on single top production, Tommaso Dorigo gives a more realistic view of the academic life than most other blogs. For some understanding of how academics feel about the travel opportunities that conferences present, and what they think about the question of whether their employer should be financing what sometimes feels like a vacation, see his recent posting on Ethical aspects of professional conference-going. I strongly endorse his recommendation of the David Lodge novel Small World.
There’s a string theory wiki out there, aimed at students trying to learn string theory, which has been set up by the Centre for Research in String Theory at Queen Mary College. Much of the site is a listing of the one thousand or so review and other papers an aspiring young theorist should read and absorb to get an idea of what is going on with string theory. Also listed are various blogs, including this one, that might save students some of this reading…
Ideally our seminar will eventually cover such material, taking a new viewpoint that makes it seems a lot less technical and scary than it usually seems. But we’re starting with more elementary stuff, e.g. Coxeter groups, Hecke algebras, buildings, Bruhat decompositions, Schubert cells and the like. Again, we’re taking a new viewpoint designed to make it less scary than usual… a big emphasis on q-deformation and groupoidification. So far we’re just doing the An case – that is, representations of Sn, SL(n) and the like. Later we’ll generalize to other Dynkin diagrams.
The seminar will probably last for at least two years. It’s hard to see precisely where it will go.
Geometric representation theory (as I understand it) is a natural extension of classical harmonic analysis in which function
spaces are replaced with various geometric alternatives, be they cohomology groups, K groups, or categories of sheaves of various
kinds (such as D-modules, perverse sheaves, coherent sheaves,…).
There are natural analogs of Fourier transforms and the classical Hecke operators, and all are realized geometrically –
one of the fundamental principles of geometric harmonic analysis
(just as for classical harmonic analysis) is that all reasonable operators are realized by “integral kernels”, which are themselves geometric objects of the same kind on a correspondence (or span).
Usually one is studying not just a space but a space with
a group action so all of the geometry is done equivariantly with respect to that group (or equivalently on the level of stacks or groupoids). Also one often introduces more refined structures (in particular gradings), coming from Hodge theory or Galois theory, leading to q-deformations. When studying semisimple groups in their many incarnations (eg over R, C, finite fields, loop groups, quantum groups etc) the spaces involved are essentially always the same – one studies flag varieties, nilpotent cones, Springer resolutions and variations on the above.
The themes and structures in the subject are
surprisingly uniform and conceptual across a broad range of questions. They’re also not at all scary or technical intrinsically, though perhaps often presented that way.
The fundamental ideas can all be explained in accessible ways, though it is hard to find literature in that spirit (I am trying to collect what informal expository
materials I can find on my webpage but there’s still a long way to go!)
In any case it’s really great to have John and James’s seminar and their excellent explanations publicly available as a resource in the subject and drawing attention to geometric representation theory and I am eagerly awaiting its further developments.
You forgot this link from NY mag:
“Simon Judes (27, string theory): Like Gob on Arrested Development! We’re basically always whining about nothing important. And then we’re absurdly happy about tiny achievements.
DK: And in every department I’ve ever been in, you have the one guy who’s essentially lost his mind. Those guys are very weird and would be great comic fodder.
AA: No other field, I think, collects as many crazies. And not just physics crazies—all kinds of crazies.
SJ: Oh, and another thing, the whole Stephen Hawking bit. Stephen Hawking is actually a rather peripheral figure in physics research.”
The other day at our physics library, I picked up a new book by Raymond Streater:
Streater, R. F.
Lost causes in and beyond physics
Berlin : Springer, c2007.
I think it should be a required reading for everyone in the topos-theoretic quantum theory business. Streater gives a thoughtful overview of quantum logic and related subjects and concludes as follows:
“Very little physics has resulted from quantum logic, trivalent logic, or Jordan algebras.”
Most sections in the book have amusing epigraphs. Here is the epigraph for the section on quantum logic, etc.:
“Science is not that easy.”
Very little physics has resulted from quantum logic, trivalent logic, or Jordan algebras.
I saw this book at GRG18 a few months ago – very nice – but this comment is somewhat behind the times.
Thanks John and David,
More expository sources about geometric representation theory would be a great help. It’s a fascinating but too little known area of mathematics, and probably has interesting implications for physics. The efforts of both of you in this direction are greatly appreciated.
“Streater, R. F.
Lost causes in and beyond physics
Berlin : Springer, c2007.
Of course, if you asked 100 physicists for a good example of a lost cause, 99 would probably cite Streater’s work. The best defence really *is* offence…
R.F. Streater has a fascinating/humorous/controversial/… web-site
Peter, in a new article in current nature magazine, it seems that Herrmann Nicolai from the German MPI for gravitational physics somwhat joins your opinions. At least the abstract reads that:
String theory: Back to basics p797
“String theory was toutet as a theory of everything”
IT WAS! (and isnt anymore..)
“And now may at last succeed as a theory of something very specific — the interactions of particles under the strong nuclear force.”
It MAY AT LEAST succeed as a theory of the strong force.
This implies indirectly that it may never succeed as a Theory of everything.
I did see that, it’s a nice article about developments in AdS/CFT. But my reading of it was that it was very careful to not take any position at all about the controversial issue of whether string theory has failed as a TOE.
Not directly relevant, but wasn’t tbere a big meeting about time at Columbia this week? Did you attend any of the talks?
The meeting wasn’t at Columbia, but all the way downtown at the New York Academy of Sciences. Not really my kind of thing, I’m too busy this week, and they were charging a $150 registration fee, so I didn’t consider going. They set up a website:
maybe at some point more info about the talks at the meeting will appear there.
Oh, sorry, whenever I see Brian Greene I think Columbia….yes, $150 is ridiculous.
Anyway I note that Sabine H. was there, and she may write a report on what she heard [about time, not about drunken physics celebrities throwing bread rolls about in the manner of Bertie Wooster……]