A simple presentation of an exceptionally simple TOE

[humanino]

If you always wanted to understand how we discover new particle, Garrett Lisi gave a delightful presentation at TED of his works :
A beautiful new theory of everything

 

[MTd2]

Did you know, or are you aware, that the Standard Model is not a subgroup his theory, but merely a subset? That means new particles should violate the standard model at tree level, that means, at the lowest apoximation, that is with no loops.It should violate all particle interactions, in all three generations. Jacques Distler pans out his most heavily criticisms on this fact.

But, I sure that no one verified if experiments can already rule out his theory, not even calculated the order of magnetude of the cross sections of any these new interactions... not even Garrett himself tried.

 

[humanino]

That's a known fact indeed, and deserves worries. But nobody really has an explanation for the CKM or CMN matrices anyways, so I would interpret the situation as most interesting.

 

[marcus]

Humanino, would you say that 80 percent of the talk is about a visual way to think about the Standard Model, and some small extensions that other people have already proposed?
That is my rough estimate.

It is about a way to understand non-verbally how Standard Particle zoo might be built up, and incrementally predicted/discovered----and to understand different ways a physicist might intuitively want to extend. One gets an idea of the way a good theorist might look at it and want to complete the symmetry.

I didn't time it with a stopwatch so I couldn't say for sure, but I guess that less than less than 5 percent of the talk is specific to Garrett's own proposals.

What he is doing is a favor to that bunch of Silicon Valley and smart media people, who get invited to TED (attendance is by invitation and it tends to bring intelligent edgy generalists).
I would say he is doing them a favor by opening a window for them to look into the head of a generic topclass theorist without being obstructed by a blackboard full of equations.

He is good at communicating. And also he is at a certain level, well, competitive. surfers can be that. My take is, that he wanted to have one of the best and toprated TED talks of this year. TED rates talks by collective audience response. You can hit high on their charts.

Not every physicist could make a hit on TED charts. You need special skill and creativity of approach. It is not like the National Geographic. So it is challenging. When you turn it on you can see that Garrett is challenged by the challenge of it. For a moment he thinks to himself "I have never done this. Will I be able to reach these people?" There is a scary moment at the start where he speaks with a different voice----no one there has ever heard his real voice and they could be fooled and think it was him. Then suddenly, he goes himself, and he is on. It is a very good talk. Not like any other physics talk I can remember, but good in its own way.

I think someone who doesn't think they need to know what they are talking about could come into this thread and start talking about what they think on this or that topic without having watched this particular video lecture. So what I am trying to point out is--- this talk is what the thread you started is about---Garrett's talk of September or October 2008. This is the focus that we can discuss, those who have watched the talk. I would say without question it is one of the great physics lectures (given the size of the problem of explaining Standard Model to intelligent people who wouldn't otherwise be interested in it, and not talking down to them.)


thanks for posting about it!

 

[Fra]

I watched the video and his slides and the visualization of the higher dimensional transformation are very appealing.

What striked me personally the most, is the impression of his methodology you get from watching this video. The impression is a guidane by mathematical beautiful patterns, and extrapolations of models guided by trying to maintain or extend symmetries, and the conviction that nature are likely to be constructed by the same mathematical beauty.

This is a way of thinking that is very different from my personal way of thinking, but it is very interesting to understand not only other peoples conclusions, but also their way of reasoning!

In all, I liked the talk and his very nice slides. Excellent intuitive visual presentation, almost artistic, like the saying that an image says more than thousand equations ;)

/Fredrik

 

[Orion1]

Based upon what I watched in this lecture, according to the Garrett Lisi model, there are 2 gravitational force spin charges: spin up, spin down.

The Garrett Lisi model for 7 charge dimensions E(7), corresponds to the Pati-Salam model with 2 new particles as 'super weak' force particles.

Pati-Salam model:
$$SU(4) \times SU(2) \times SU(2)$$

According to Wikipedia, these 2 new particles corresponds to neutral 'sterile neutrinos', a sterile neutrino and a sterile anti-neutrino.

And at 8 charge dimensions E(8), there are 18 new coloured strong force particles, for a total of 20 new particles.

What does the symmetry pattern appear like for E(9)?

Reference:
http://en.wikipedia.org/wiki/Pati-Salam_model"

 

[humanino]

Thank you Marcus for the comments. I fully agree with them. I think it is also interesting to contemplate the viewpoint of a relative "outsider" to mainstream physics. This presentation tells a lot about Garrett's personality as well.

What does the symmetry pattern appear like for E(9)?

What is E(9) ?

 

[Autochthon]

Perhaps someone can clarify let me start simple is he describing a single common class of entity that is uniquely defined by it's movement through various degree's of freedom as defined by an E(8) shaped space? or multiple classes each of whose properties and interactions are described by that shape? From his coral analogy at the start I took it he meant the former.

 

[Orion1]

I located the Garrett Lisi model in Wikipedia, listed in reference 1, and his original arxiv paper, listed in reference 2.

Reference:
An Exceptionally Simple Theory of Everything - Wikipedia
An Exceptionally Simple Theory of Everything - Garrett Lisi - arxiv
E7_(mathematics) - Wikipedia
E8_(mathematics) - Wikipedia
Lie group - Wikipedia

 

[MTd2]

What is E(9) ?

A found this on wikipedia"In geometry, a semiregular k21 polytope is a polytope in (k+4) dimensions constructed from the En Coxeter group, and having only regular polytope facets. The family was named by Coxeter as k21 by its bifurcating Coxeter-Dynkin diagram, with a single ring on the end of the k-node sequence.

Thorold Gosset discovered this family as a part of his 1900 enumeration of the regular and semiregular polyopes, and so they are sometimes called Gosset's semiregular figures. Gosset named them by their dimension from 5 to 9, for example the 5-ic semiregular figure.

The sequence as identified by Gosset ends as an infinite tessellation (space-filling honeycomb) in 8-space, called the E8 lattice. (A final form was not discovered by Gosset and is called the E9 lattice: 621. It is a tessellation of hyperbolic 9-space constructed of (∞ 9-simplex and ∞ 9-orthoplex facets with all vertices at infinity.)"

http://en.wikipedia.org/wiki/Semiregular_E-polytope

 

[MTd2]

The use of this E(n), n>8 is due to the resemblance that the Coxeter representation of some groups have with the ones of E(8), E(7), E(6).

Some people that study M-Theory like these groups. There is a fairly famous one, from last year, that argues supergravities, superstrings and stuff, can be derived from E(11):

http://arxiv.org/abs/0705.0752v1

 

[humanino]

So with infinite dimensional Lie algebras, you would have an infinite number of interactions ?

 

[MTd2]

So with infinite dimensional Lie algebras, you would have an infinite number of interactions ?

Why are you saying that?

 

[Orion1]

It turns out that they mostly fall into four infinite families, the "classical Lie algebras" An, Bn, Cn and Dn, which have simple descriptions in terms of symmetries of Euclidean space. But there are also just five "exceptional Lie algebras" that do not fall into any of these families. E8 is the largest of these.

E(n) Lie algebras have an infinite number of families.

The E(8) Vertices total number 240, is equivalent to the total number of individual charges and fundamental particles in the Garrett Lisi model, including the 20 new fundamental particles.

E(9) is a 'E8 lattice' Euclidean 8-space lattice (E8), (∞ 8-simplex and ∞ 8-orthoplex facets), with the largest exceptional Lie algebra Gosset semiregular polytopes, with and an infinite number of Vertices, therefore, according to the Garrett Lisi metaphysical pattern, it is predicting an infinite number of charges and fundamental particles and interactions and apparently cannot be visually depicted.

Is a Gosset E(9) Euclidean 8-space lattice (E8) really capable of breaking symmetry into a subset Gosset polytope Garrett Lisi E(8) TOE model?

Attachment: left Gosset E(8) with Vertices, right Garrett Lisi E(8) with new particles.

Reference:
Semiregular_E-polytope - Wikipedia
Lie group - Wikipedia

 

[MTd2]

Oh, what Garrett uses is the algebra of the group e(8), that is, it gives the possible combinations that one particle can have with each other. In that page of wikipedia, what is discussed are polytopes, that is, kinds of polyhedra in higher dimensions, except that in that case, it follows a certain formula, a certain pattern of coxeter-dynkin diagram, to generalize in higher dimensions.

Now, we have to distinguish a few things,

1. All polyhedra in that sequence are finite, except for the last 2, which are infinite
2. The 3rd last polytope, 4_21, is what Garrett lie uses.
3. The 2nd last polytope, 5_21 polytope, turns out to be also the E(8) lattice. The smaller, polytopes, in that sequence, are just finite things.
4. The last polytope, E(9) is also infinite, except that the space in which it is embended, it is infinite. In that case, it is a lattice in a hyperbolic space.
5. E(10) and beyond are not even polytopes, just algebras.
6. Calling anything E(n), n>8, is an abuse of language, because an exceptional group or algebra, is at first place a simple algebra. A simple algebra is a kind of "prime number" of non abelian algebras. The only normal subgroups, or sub algebras, are the idendity and itself.
7. But calling E(n), n>8, is useful to some people because they can remember how they behave easily.
8. E(11)

*So, what garrett algebra could do with E(8) lattice is to map n-dimensional planes, to other n-dimensional planes, by telling what goes to where and such.*-> wrong

 

[humanino]

Why are you saying that?

Because you will have an infinite number of generators of your algebra, hence an infinite number of gauge fields. I am just questioning whether it can be a physical proposal, because I can not imagine how one can convince oneself of the existence of an infinite number of possible interactions, considering how long and difficult it is to study just one.

 

[Orion1]

Calling anything E(n), n>8, is an abuse of language, because an exceptional group or algebra, is at first place a simple algebra.

For purposes of this thread, simply calling E(n) as an 'Element' with n dimensions, instead of an 'exceptional' Lie algebra, should be appropriate, since the original exceptional labeling does not use any brackets.

 

[MTd2]

So, following the pattern of coxeter dynkin diagrams k_21 semiregular polytopes, and calling them E(k+2), we have the following structures:

0<n<9 -> polytopes/ finite algebras
n =9 -> E(8) lattices/ infinite dimensional algebra
n = 10 -> E(9) hyperbolic lattice/ infinite dimensional algebra
n=11 -> infinite dimensional algebra, conjetured to be the symmetry group of M-Theory
n>11 -> infinite algebras, without any known use.

I found this here:

http://en.wikipedia.org/wiki/En_(Lie_algebra)

PS.: Interesting thoughts guys.

 

[MTd2]

For purposes of this thread, simply calling E(n) as an 'Element' with n dimensions, instead of an 'exceptional' Lie algebra

Yes, and also the other 2 exception Lie algebras do not have an E, that is G_2 and F_4

 

[Orion1]

Is a infinite dimensional Kac–Moody algebra M-Theory Element E(11) really capable of breaking symmetry into a subset Gosset polytope Garrett Lisi Element E(8) TOE model?

Reference:
En_(Lie_algebra) - Wikipedia
M-theory - Wikipedia

 

[MTd2]

Correction:

Alright, so your E, is E(n), where n=k+1.