Technocrat

Whither Garrett Lisi and the E8 theory of everything?

bi-ker-shi
Thu Jan 24 18:27:37 -0800 2008
Physics.
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Technocrat readers may recall how Garrett Lisi and his exceptionally simple theory of everything blew our minds away back in November. So what happened next?

One commentator Macus du Sautoy thinks that there is a consensus that it is impossible to use E8 in the way he was hoping and produce a consistent model that reflects reality. Read what he has to say here. Personally I am not so sure.

There seems to be two fundamental ideas in Garrett's work. One of these is the idea that due to the exceptional properties of E8, it's possible to represent fermions and bosons, or spinors and tensors within a single Lie Group framework. Read what Sabine Hossenfelder had to say about this here. String theorists are inclined to be hostile to this idea because they have their Super Symmetry where they combine fermions and bosons using an alternative mathematical construct called a super lie group. So far however I have not seen anything that convinces me that the idea is flawed.

The other idea was that symmetries present in the standard model could all be derived from E8. In his paper however, Garrett acknowledges that he can't quite get the three generations of fermions to fit into E8. Most commentators are very sceptical on this point. Jacques Distler, a string theorist and very eminent professor has contributed most to this debate, see here. Garret explains in this blog that he will be working hard in the next few months to answer the criticisms.

Something I noticed in these debates was that there are in fact multiple representations of the E8 group (read here distinct lie groups that inherit from a common parent), and that there was some confusion as to which one Garrett was using. In previous Distler blog, Garrett indicates that it is the split real form of E8, not the EIX form as indicated in his paper.

Other criticisms of Garret's theory are that it violates the Coleman-Mandula theorem by mixing up internal and external states. I think this is not relevant, ever since this theorem came out physicists have been inventing loopholes. String theory for example gets around it by the fact the particles are no longer points, but extended objects. Garrett's theory is essentially silent on the issue and it's unfair to be reading his mind on this one. If he can address the more important issues, then he can address this one too.

Personally I have my doubts about it all. I think that if Garrett can solve the fermion generations issue, he still will not have a mathematical model that can do practical things like predict particle masses etc.

Symmetry groups are really a distillation from something more complex. The split form of E8 for example represents the symmetries in a system containing a pair of octonions (hyper complex numbers) and a variety (think of a mobius strip, the variety is the twist angle). Think of a normed octonionic field in space time (the first octonion) that has a metric based differential auto-correlation (the second octonion). Now describe this system in terms of a stochastic differential equation. Prove that the solutions in the limit are equivalent to quantum field theory. Do that Garrett and you really will be the next Einstein.

Whither Garrett Lisi and the E8 theory of everything?
rubycodez
Thu Jan 24 22:05:07 -0800 2008
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besides no quantization no symmetry breaking and no cosmological constant, not describing our universe then though maybe all possible ones.

in a vague, handwavy way

Thomas Lord
Thu Jan 24 23:32:03 -0800 2008
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An attractive thing about an E8 hypothesis is that it is "maximal" in the sense of being the most complex possible example of a particular fairly fundamental class of structures.   A kind of "everything that might possibly exist, does" hypothesis, for some slice.

-t
in a vague, handwavy way
bi-ker-shi
Fri Jan 25 20:40:02 -0800 2008
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There are infinite dimensional lie groups you can make do just about anything. El Naschie came up with an idea similar to Garrett some years ago but using a transfinite E8 exceptional group.

I believe that you can't really model what is happening by looking at the symmetry group alone. E8 split form is known as the 'octo-octonionic projective plane' or more exactly E8 is the set of symmetry transformations on that construct. Think of it like an octonion field in space time with a spinning soliton. Each point has a different value and there is a relationship between this value and the way it is changing.

The problem with octonions though is that the octonions are non associative meaning you can't build a linear algebra that represents them the way you can with Lie groups. (You cannot represent them in terms of a restricted set of matrices.) Linear algebras factorise into Eigen vectors and Eigen values. Symmetry breaking occurs when something makes these Eigen vectors different, i.e. a hyper ellipsoid instead of a hyper sphere.

The octonions though do form the largest possible normed division algebra. This seems to be important because of the renormalisation group, (the way things transform at different scales). Renormalisation requires a non-linearity like the way atoms in a bar magnet all have a constant magnetisation, only the orientations vary from place to place.

BTW I may not have replied to your posts on Solaris, but I did read them with interest.
Whither Garrett Lisi and the E8 theory of everything?
disco
Fri Jan 25 10:45:11 -0800 2008
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I was wondering what happened with this just a couple of days back, so thanks for posting this. It's all very intriguing in a way-over-my-head kind of way.
Whither Garrett Lisi and the E8 theory of everything?
bi-ker-shi
Fri Jan 25 19:40:59 -0800 2008
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One of the references in Garrett's paper concerning the octonions is easier to read. Like you, there are gaps in my knowledge, so writing anything meaningful requires a lot of hard work researching, and alas I almost certainly did not get it completely right.

Professor Jacques Distler is quite sceptical as distinct from prejudiced and has identified major issues in the group theory. Garrett will need to be a Houdini to escape from these issues. Good luck Garrett and many thanks Jacques for putting in the effort.
 

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