Professor Jacques Distler has revived his old attack on Garrett Lisi’s idea for unification using the exceptional Lie structure E8. It’s becoming funny to watch the arguments. Jacques begins with the quotation:
“It is difficult to get a man to understand something when his livelihood depends on him not understanding it.” — Upton Sinclair
Jacques goes on (prior to the mathematical discussion):
Skip and I wrote a paper, last year, which proved that Garrett Lisi’s “Theory of Everything” (or any E8-based variant thereof) could not yield chiral fermions (much less 3 Standard Model generations worth of fermions). Anyone with training in high energy theory instantly apprehends the consequence that this “theory” cannot, therefore, have anything remotely to do with the real world. Unfortunately, if your PhD is in pure mathematics (or, apparently, in hydrodynamics), this may not be immediately obvious to you.
Skip has the unenviable task of lecturing on our paper at a workshop, next week, with Garrett in attendance. (Well, OK, the workshop is in lovely Banff Alberta, so perhaps some envy is warranted.) This post is designed to help him fill in the dots. It contains only material which — to someone schooled in high energy theory — is of an embarrassingly elementary nature.
Jacques, you see, is responding to Garrett’s new arXiv paper, An Explicit Embedding of Gravity and the Standard Model in E8, which claims:
The algebraic elements of gravitational and Standard Model gauge fields acting on a generation of fermions may be represented using real matrices. These elements match a subalgebra of spin(11,3) acting on a Majorana-Weyl spinor, consistent with GraviGUT unification. This entire structure embeds in the quaternionic real form of the largest exceptional Lie algebra, E8. These embeddings are presented explicitly and their implications discussed.
So Garrett is claiming to be able to embed fermions within an E8 symmetry, while Jacques and Skip claim to disprove the idea that any chiral (spin-handed) fermions can be produced by an E8 algebra. Being a string theory fanatic against alternative ideas, as we suggested in the previous post, Jacques who is an arXiv adviser finds no problems (unlike Dr Woit, in the recent case of trackbacks to string theory papers) in leaving a critical trackback to Garrett’s arXiv paper.
Garrett, like me, surfs and windsurfs, but I don’t have any enthusiasm for his paper which predicts nothing checkable, explains no particle masses, no coupling parameters, no mixing angles, in short nothing. He claims to show that E8 can be used as an ad hoc model to represent the patterns of fundamental particles, although Jacques and Skip dispute it by showing that E8 will inherently yield non-chiral, “mirror” fermions. In any case, it’s an ugly, ad hoc piece of speculative framework modelling which runs completely counter to Occam’s Razor and to the primitive notion of building theories on facts rather than the time-wasting hype from fiddling around with Platonic mathematical patterns to “describe” directly unobservable features of the world in an uncheckable, non-falsifiable way.