A paper by Garrett Lisi that John Beaz will enjoy

[Edward C. Jones]

"An Exceptionally Simple Theory of Everything" by A. Garrett Lisi.
http://arxiv.org/abs/0711.0770

He uses the Lie Algebra E8.

 

[Phillip Helbig---remove CLOTHES to reply]

In article <aeadnSDbTupug6DanZ2dnUVZ_rSrnZ2d@comcast.com>, "Edward C.
Jones" <edcjones@comcast.net> writes:

> "An Exceptionally Simple Theory of Everything" by A. Garrett Lisi.
> http://arxiv.org/abs/0711.0770
>
> He uses the Lie Algebra E8.

> Subject: A paper by Garrett Lisi that John Beaz will enjoy

Indeed. John mentioned him in This Week's Finds a while back (and from
Lisi's website, it appears that appearing in This Week's Finds was
almost as exciting for Lisi as developing the TOE) and John is mentioned
in the acknowledgments of the paper.

The relationship between E8 and physics is not new. However, Lisi might
have taken things farther than anyone else.

 

[john baez]

"An Exceptionally Simple Theory of Everything" by A. Garrett Lisi.
http://arxiv.org/abs/0711.0770

He uses the Lie Algebra E8.

Yeah, I'm enjoying this paper. I'm not especially enjoying the ridiculous media hype surrounding it, e.g. the Fox News report titled http://www.foxnews.com/story/0,2933,311952,00.html". Sure, it's fun... but there are way too many unsolved problems with Garrett's ideas to warrant such excitement just yet.

For example, so far his theory has nothing at all to say about particle masses, the http://en.wikipedia.org/wiki/Cabibbo-Kobayashi-Maskawa_matrix" that any theory must either calculate or take as adjustable parameters. Garrett's theory seems to have no adjustable parameters. But, he doesn't calculate these numbers, either.

There are also a bunch of other issues. I hope to say more someday, when I understand this stuff better. I have a grad student working on grand unified theories, John Huerta. We're starting to read Lisi's paper.

 

[Bryan Bishop]

On Nov 16, 7:14 am, "Edward C. Jones" <edcjo...@comcast.net> wrote:
> "An Exceptionally Simple Theory of Everything" by A. Garrett Lisi.http://arxiv.org/abs/0711.0770

I remember noticing a Tegmark reference at the end of the paper. This,
along with the Baez mention, is all that I can relate to as of yet. It
would be great if any of the gurus could list off some more
publications to read, in the hopes of maybe one day understanding the
mathematics.

- Bryan
http://heybryan.org/

 

[john baez]

It would be great if any of the gurus could list off some more publications to read, in the hopes of maybe one day understanding the
mathematics.

To understand this stuff you mainly need to understand the theory of root systems for simple Lie algebras, and its application to exceptional Lie algebras.

For the former, it's hard to beat J. Frank Adams' book Lectures on Lie Groups. For the latter, it's hard to beat Adams' book Lectures on Exceptional Lie Groups.

The first book is full of stuff that every mathematician should know. The second is more specialized... but it's precisely this stuff that Lisi uses.

You might also want some warmup on how these ideas are used in grand unified theories. Howard Georgi's Lie Algebras in Particle Physics is good for that. Mohapatra's book Unification and Supersymmetry is also very good.

At a more elementary level, there's my course on "[URL
Clifford algebras and algebraic patterns in the Standard Model[/URL]. This explains the basics of the SU(5) GUT. Lisi's website is also full of expository material. Eventually my grad student John Huerta will write a paper on the algebra behind grand unified theories, and that should also help.

 

[Ivan Urwin]

Novice posting. Skip this if you want a serious discussion or have little time, etc.

Thanks for the links John Baez. I have a slow modem but downloaded some of the files and hope to look at them today - son's birthday party etc permitting.

I find it hard to believe that physics is ready for a theory of everything. I tried to understand the gas law recently and when I did, I realized that those teaching it didn't. But then, I suppose it is perfectly possible that the physics world has bypassed some basics to get to things that are more complicated.

(Note about the gas law. Everyday temperature is energy per degree of freedom; though for subatomic physics I guess you'd have to define it differently. So the gas constant - R, in joules per mole kelvin - should have a dimensionless value, since a mole is just a number in the same way that a dozen is 12, a score is 20, a gross is 144, etc.
Factoring out the constant, we get a gas constant in different units - k, in joules per kelvin - which is just a ratio of two energy units. Depending precicely on your definition of temperature, the conversion constant between joules and kelvin can vary, but a good candidate is k/2. And when that is used, the gas constant the evaluates to a value of k/(k/2)=2. Reflection on why the gas constant should be 2 then provides some insight to the nature of the constant. If a window is closed, the pressure at the window results from an assumption that gas molecules bounce back at the same speed and the 2 results from a reversal of a molecule's direction when it hits the window. In the case of an open window, the 2 results from the momentum exchange arising from molecules exiting a room and similar molecules but with opposite direction entering the room.)

So how can we be at a stage in physics, where we are solving the structure of the universe, when people are being taught "so many kilojouse per kilomole kelvin" for a constant that is essentially 2?

Nevertheless. I read Garrett Lisi's paper, having come across it as a Joe Public reading a bit in a newspaper and following a web link to his paper. Obviously it makes little sense to somebody who has just dived in at the deep end, and hasn't yet learned how to swim, let alone surf.

But I was wondering if somebody could just set me straight on some of the basics here. As I understand it, there are several steps to understanding the nature of the universe: what is the structure of space, what can exist at those "points" in space, and how do thing in space interact.

I understood it all to mean that "the structure of space" is a sort of lattice, a multidumensional fishnet, checkerboard, chickenwire of connected points that can contain stuff. The question of "what can exist at those points" is Garrett Lisi's application of E8, where he has maybe found an elegant way of embedding all the known particles in a single copy of E8 rather than have a copy of E8 describing some particles and then creating larger structures by having to incorporate other categories of particles, and then further pairing this back again, finding a substructure to avoid having a model that incorporates non-existent particles. The question of how stuff interacts seems to depend on existing operations defined in the mathematical structures defining this "structure of space" and in E8.

That is how it came across to a complete novice trying to make a bit of sense of Garrett Lisi's stuff; but without any knowledge of that maths, I am clearly biting off more than I can chew, and am likely to choke on it.

If I have understood correctly, E8 is only used to describe the "what can exist at those points". For "the structure of space", he is happy to use existing structures, under the assumption that these give the correct shape to space to be consistent with astronomy and relativity etc. Mathermatical operations [the Lie bracket?] in E8 define the interaction between particles etc. ie the behaviour of things in space.

The genius of Garrett Lisi's work is therefore to have hopefully found a way of embedding all the know particles in a single copy of E8 without contravening the physical laws of known particle existence and interaction. The problems are that (1) the embedding is not described explicity, particle to E8 element, but merely as collections of particles to E8 substructures - something likely to change as a sort of pseudo progress, but not really helping as the nature of the problem is whether the embedding is possible and correctly describes nature, not an actual element to element mapping, which symmetry will allow in many ways, and (2) the embedding is not described exactly or completely.

Criticism has been raised that the model does not say anything about masses.
If masses arise from the mathematic structure of operations and the structure is correct then calculations should give correct masses. I don't see a problem with not doing the calculations. Surely the real question is whether the embedding of all known particles in E8 contravenes the observed interactions of particles; and these interactions are described by a so called standard model; and Garrett Lisi hopefully embeds the standard model in E8. So what really matters is whether the tentatively described embedding is actually possible and if the description of the embedding is incomplete, to select a working choice for parts glossed over, in order to demonstate the particle embedding in E8.

I don't know if I am talking rubbish or not. As I said, I am an outsider that just looked at his paper folling a link from newspaper hype (Daily Telegraph in the UK).

I didn't understand much at all of the theory. It appears particles correspond to vectors in E8. The quantum idea seems to give rise to the idea of base vectors, where you cannot have a fraction of a base vector but you can have multiples of it. If these vectors in E8 are a representation of physical particles, eg electrons, what does that mean in real life? I take it to mean you cannot have half an electron, but you can have two electrons. What I don't know from this E8 stuff is whether you can have two at the same place at the same time. If you can, then presumably infinite desity is a possibility and if you can't then there is a maximum density possible of one heaviest particle for each lattice point of space.

If somebody could put the whole 248 dimension stuff into context I'd appreciate it. If something can take 4 values I can imagine it as {1,2,3,4} and call it one dimensional, imagine it as {(0,0),(0,1),(1,0),(1,1)} and call it two dimensional, image the corners of a tetrahedron and call it 3D, or image 4 axes, {x,y,z,w} and call it 4D. Are we saying there are 248 basic building blocks? Can a point in space simultaneously contain 1 of these, any combination, any multiple, or any combination of any multiple?

(I guess this will become clear when I read the links from John Baez. But due to all the hype, I think there are going to be lots of annoying non-experts - like me - asking these sort of stupid questions. Who doesn't want to know what the world is made of?)

My other question of basic understanding is just whether I am right in understanding that E8 describes only what can be at a point in space and that another mathematical structure - the world manifold comes to mind from memory - describes the actual shape of space, what I think of as a sort of multidimensional lattice, or fishnet, or brickwork pattern, or hexagonal chicken wire or whatever.