Several people have been posting, here and more broadly, about Garrett Lisi’s new candidate unified theory of fields and gravity. (Even slashdot seems to have picked it up) This got encouraged by Lee Smolin, of loop quantum gravity fame, getting publicly excited about it, and it makes for great news because Lisi isn’t currently a practicing physicist — he’s currently a surf bum with a PhD. The biggest problem is that this paper is wrong in some rather key ways.
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. 🙂
Yonatan Zunger’s Blog 
I have a feeling physicists are taking over the surf bum community more and more; I was rather confused the last time I hung out in Santa Cruz and the surfers were getting high and discussing manifolds.
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.
I have a feeling physicists are taking over the surf bum community more and more; I was rather confused the last time I hung out in Santa Cruz and the surfers were getting high and discussing manifolds.
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.
Hey… I was trying to invite you to a housewarming on Sunday, but couldn’t find a current e-mail address for you. Ping me if you get a chance, I’ll send you coordinates.
Hey… I was trying to invite you to a housewarming on Sunday, but couldn’t find a current e-mail address for you. Ping me if you get a chance, I’ll send you coordinates.
Ditto on the helpful explanation. With my embarrassing lack of knowledge of group theory, I of course don’t get the details, but I get the general sense.
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.
Ditto on the helpful explanation. With my embarrassing lack of knowledge of group theory, I of course don’t get the details, but I get the general sense.
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.
Hmmm… skimming over the paper, I was reminded of Kepler and his Platonic Solids.
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.
He notes that this theory predicts a couple of new particles/fields, X and w, “which presumably have large masses impeding their measurement.” Later, he says, “The theory has no free parameters. The coupling constants are unified at high energy, and the cosmological constant and masses arise from the vacuum expectation values of the various Higgs fields…”
Does his theory predict the masses of the particles or not? (If not, it’s not much of a grand unified theory…)
Nope. He’s got the unification part, but there’s no explanation of the spontaneous symmetry breaking, which you would need in order to predict particle masses.
Does that mean his paper constitutes a “gross unification theory?”
What I didn’t understand from your summary of what’s wrong with this paper is whether you agree with the claim that, at least, the particular unification that he came up with is especially striking in its simplicity. That is, I’m wondering whether you think that the claim is true, but the work is still no good due to all those flaws, or that even the claim itself is false, because, if allowed such flaws, any graduate student could have easily come up with that.