For a long time, the physics part of my brain has been fast asleep. But I had an idle moment recently, and decided to have a look at the recent issues John Baez’s excellent column, This Week’s Finds in Mathematical Physics. Baez — a mathematical physicist specialising in quantum gravity and category theory — has been a very visible figure in the physics and maths communities online for years, and is known for his prodigious output both as an expositor and a researcher. He has the rare ability to explain often extremely abstract concepts in very concrete terms. (His student Derek Wise seems to have inherited this ability — I read his recent paper and finally understood Cartan connections in terms of hamsters inside rolling spheres.)
I highly recommend his site to anyone looking for a quick introduction to almost any topic related to modern mathematical physics from general relativity to topos theory. The SF fans here may also be amused by the fact that Baez has collaborated on a couple of papers with the Australian AI of SF, Greg Egan.
One of the gems on his site is the page Open Questions in Physics, the Frequently Unanswered Questions of hard science. The big one is, of course, the riddle of quantum gravity, but Baez lists many less well known ones as well, such as sonoluminescence. Baez gives an especially lucid treatment of the open problems in cosmology and particle physics, with many references. Definitely worth checking out if you want to get a clear picture of modern physics in terms of what we don’t know.
My favourite open physics puzzle is actually somewhat less grandiose — namely, the so-called Brazil nut effect and its even more puzzling reverse. Basically, the question is why the biggest particles end up on top when a granular material containing a mixture of objects of different sizes is shaken. In spite of the huge practical importance of this problem (related granular flow effects cause grain silo collapses), no one has yet produced a satisfactory explanation of this, which strikes me as wonderfully bizarre. This one, at least, won’t be cracked by LHC…