He starts with the realization that you can express the equations of (classical) general relativity as a gauge theory of SO(3, 1), which is both true and very important, and then tries to do the natural operation of unifying this SO(3, 1) gauge group with various other groups to form a nice unified theory. He ends up with something he calls E8, which seems awfully nice from a mathematical perspective, and is very elegant. There are only two problems.
- His group isn't E8. Since SO(3,1) is noncompact, it should be pretty obvious that it can't embed in a compact Lie group, and it doesn't. He ends up with something that looks sort of like a noncompact cousin of E8... except that all of the Dynkin diagram--based classification that he uses for his calculations doesn't actually work properly for noncompact groups. (The basic theorem that Dynkin diagrams can describe Lie algebras is very dependent on compactness -- and to see why, if you work out the Dynkin diagram for the Virasoro algebra, it looks the same as the diagram for SU(2). Despite the Virasoro algebra being infinite-dimensional and SU(2) being only 3-dimensional.)
- But assuming that this is fixable, his group isn't really E8 but some other group, and everything else with his group theory is OK (I didn't sit down to check this)... gauge theories of noncompact gauge groups aren't renormalizable. Not even slightly. This E8 unification is pretty and all from a classical perspective, but if you try to quantize it everything diverges. (After all, if you could do that to a noncompact group, you could do it to SO(3, 1) as well and write a working theory of quantum gravity in ten minutes)
Anyway, that was really technical and is mostly for the reference of any physicists who still read this. The non-technical version is that it makes for a great news story and all, but this is the sort of idea that most high-energy physicists come up with sometime during grad school, think about for a few minutes, and then realize why it doesn't work.
What's more amusing is watching Lee Smolin go off and praise it, just because it's a non-string-theory theory of quantum gravity. :)
us "normal folk" appreciate the explanation
Anonymous
November 16 2007, 14:34:55 UTC 8 years ago
-Otter
P.S. Side-swiping your state and heading for Seattle tonight on holiday. See ya.
November 16 2007, 23:06:55 UTC 8 years ago
Likewise, thanks for the explanation. I'll send you a draft of my paper "Proof of God: The Theory of Maximum Spite" soon, in which I chronicle how the probability of the number of sublimely unfortunate occurrrences is outside of the scope of human providence.
November 17 2007, 02:20:01 UTC 8 years ago
November 17 2007, 03:49:00 UTC 8 years ago
I liked Smolin's recent book ("The Trouble with Physics"), but getting so excited about something like this that it gets into the media seems a bit unprofessional.
November 17 2007, 04:09:54 UTC 8 years ago
Some choice quotes:
"This is a somewhat arbitrary choice, selected for leaving W3 and color invariant."
"This action works very well for one generation of fermions. The action for the other two generations should be similar, but is related by triality in a way that is not presently understood well enough to write down."
"The action for everything, chosen by hand to be in agreement with the standard model..."
"Currently, the symmetry breaking and action for the theory are chosen by hand to match the standard model -- this needs a mathematical justification."
It seems like he's found a way to make much of the picture fit into a pretty box, if you just squint and file down a couple of the pesky parts that stick out too far.
November 17 2007, 04:13:35 UTC 8 years ago
Does his theory predict the masses of the particles or not? (If not, it's not much of a grand unified theory...)
November 17 2007, 05:02:58 UTC 8 years ago
November 18 2007, 02:14:13 UTC 8 years ago
November 18 2007, 02:16:10 UTC 8 years ago
November 18 2007, 07:01:58 UTC 8 years ago