An Exceptionally Simple Theory of Everything

[ccdantas]

There are questions at page 39 and also at the end, I'm almost finishing it. He also has time to continue with 3 extra slides at the end.

I recommend listening to the audio; the talk clarifies several points.

 

[ccdantas]

I think there was some joke right at the end?

I cannot understand it. Could someone tell me? ;)

 

[marcus]

i will go back and try to find the joke. what I remember is Abhay Ashtekar saying that the Coleman-Mandula no-go does not apply because it is a "totally different framework" and Garrett is kind of chuckling that at Sabine Hossenfelder blog the discussion has gone on to some 160 comments and the "string theorists and a few particle theorists" still have not understood that it is, as A.A. immediately perceived, a different framework, and are still hammering at him about C-M. Maybe there was an ironical chuckle there but I don't remember a burst of laughter. I will go back and look for something else.

I went back and there ARE a couple of bursts of laughter at just this point---where Garrett says he will not bother with the last slide, the Coleman-Mandula slide, unless someone insists and Jorge says "I insist!". And then there are some ironical remarks ("this has been discussed a lot mainly on the internet, but who reads that sort of thing ") and some more laughter. The basis of the joke is that C-M does not actually apply to what G.L. is doing, but on blog-threads he gets constantly harrassed by string/particle minded folks about the C-M---which they seem to think makes what he is doing illegal. And since C-M does not really apply he didn't want to discuss it, but Jorge twists his arm a little. The joke is that mentioning the C-M is extraneous to the talk, but he has to do it anyway because it has been raised as an issue.

Was that the laughter (right near the end) that you were asking about, Christine?

 

[marcus]

Here is the direct link to the PDF (this is to the second improved PDF with the extra slides.)
http://relativity.phys.lsu.edu/ilqgs/lisi111307_2.pdf
Here is the direct link to the audio.
http://relativity.phys.lsu.edu/ilqgs/lisi111307.wav

I now feel confident to recommend that everybody here at Beyond forum should listen to this talk, for me I should listen several times. Anybody at all interested in Unification and Quantum Gravity in the normal everyday number of spatial dimensions.

The main people besides the moderator Jorge who are commenting and asking questions are Abhay Ashtekar and Lee Smolin. I missed Rovelli, who often takes part in ILQGS

 

[jal]

Hi garrett!
From the way you organized your slides and audio I would say, to paraphrase bee, "... a little bit of german ...?
You said at bee's blog ...
"More technically, (I think) we're splitting E8 into the bosonic subgroup part:
SO(8) + SO(8) and the fermionic part is the coset space,
E8/(SO(8)+SO(8)) But I'm doing this on the Lie algebra level and haven't worked it out topologically."
---------
Lot's of work left to do.
Have you got a team of helpers? Or are you thinking that individuals will independently work on this E8 model without "... a little bit of german ...?
jal

 

[strangerep]

what I remember is Abhay Ashtekar saying that the Coleman-Mandula no-go does not apply because it is a "totally different framework" and Garrett is kind of chuckling that at Sabine Hossenfelder blog the discussion has gone on to some 160 comments and the "string theorists and a few particle theorists" still have not understood that it is, as A.A. immediately perceived, a different framework, and are still hammering at him about C-M.

I went back and there ARE a couple of bursts of laughter at just this point---where Garrett says he will not bother with the last slide, the Coleman-Mandula slide, unless someone insists and Jorge says "I insist!". And then there are some ironical remarks ("this has been discussed a lot mainly on the internet, but who reads that sort of thing ") and some more laughter. The basis of the joke is that C-M does not actually apply to what G.L. is doing, but on blog-threads he gets constantly harrassed by string/particle minded folks about the C-M---which they seem to think makes what he is doing illegal. And since C-M does not really apply he didn't want to discuss it, but Jorge twists his arm a little.

IMHO, discussion involving C-M is relevant, not deserving of ridicule, in the following sense...
The paper is titled "An Exceptionally Simple Theory of Everything". But there does not
seem to be a usable method to calculate scattering cross-sections. OK, C-M might not apply,
but how then can one wield the "theory" in any practical way? Is it perhaps premature to
call it a "theory"? Maybe "...towards a partial framework..." is a better way to describe it?

 

[marcus]

The paper is titled "An Exceptionally Simple Theory of Everything"...

I suppose ten years of string hype (if it was taken seriously) may have prepared some of us to read G.L.'s title with utter solemnity. My initial reaction, by contrast, was that the title was quite funny and contained two shameless puns as well as the obvious ironical reference to stringy promises of yore.
The group E8, which is the main actor, is technically a SIMPLE group and it is one of the EXCEPTIONAL groups. And "Theory of Everything" makes one immediately think of Brian Greene and a decade of unsupported hyperbole about fashionable but fruitless research.

So I took the title as witty and just a wee bit satirical---the gross puns making clear the burlesque element.

Here at PF I remember my first post on this thread was initially just laughing about the title, but after a few minutes that seemed like a superficial reaction, so I edited out my appreciation of the humor.

I would encourage all LQG authors, or more generally non-string QG authors, when they get around to including matter so that they are working with a quantum dynamics of geometry AND matter, to use the phrase "Theory of Everything" every chance they can, because it is such a nice ironical echo from the string glory days.

I hope you saw today's ILQGS seminar talk, which has another very funny title:

A CONNECTION WITH EVERYTHING

got to love it, right?

 

[garrett]

Exactly so.

 

[hch]

RG running

hi marcus,

i think the connection to the truncated flow RG running of QEG is not quite as nice as you seem to hope. as far as i remember, reuters biggest problem is the fine tuning issue of the real world RG trajectory. and per se, it would again require anthropic reasoning.

IF a theory predicts the correct starting point in the UV, THEN things should look much better. but again, as far as i understand these need to be extremely finely tuned initial conditions and i do not see at all that they come out from any kind of unified theory at the moment.

 

[marcus]

... reuters biggest problem is the fine tuning issue of the real world RG trajectory. and per se, it would again require anthropic reasoning.

IF a theory predicts the correct starting point in the UV, THEN things should look much better...

this is off-topic in this thread. Reuter and Percacci work on asymptotic safety is different from Lisi's work. We already have some threads about their work, where your post would be an interesting contribution---or we could start a new thread for critique of the asymptotic safety papers.

I think it is very appropriate to be scrutinizing Reuter's papers at this point and looking for gaps and weak spots. I hope you have read the recent papers from him and Percacci and want to explain, point me to specific pages where you think the problems are etc.
Let's find or set up a thread where that won't be a distraction from the main topic.

 

[hch]

this is off-topic in this thread. Reuter and Percacci work on asymptotic safety is different from Lisi's work. We already have some threads about their work, where your post would be an interesting contribution---or we could start a new thread for critique of the asymptotic safety papers.

I think it is very appropriate to be scrutinizing Reuter's papers at this point and looking for gaps and weak spots. I hope you have read the recent papers from him and Percacci and want to explain, point me to specific pages where you think the problems are etc.
Let's find or set up a thread where that won't be a distraction from the main topic.

sorry, it was not my intention to discuss asymptotic safety. i merely wanted to point out, that a theory that requires a large lambda at high scales, while it is in a sense compatible with asymptotic safety, is not automatically of any help there unless it is fine-tuned. i just found your optimistic statement, that this combines nicely with asymptotic safety a bit too bold.

 

[marcus]

...i just found your optimistic statement, that this combines nicely with asymptotic safety a bit too bold.

I dare say that something I said earlier in this thread COULD have been too bold, and in need of qualification.

If you wouldn't mind, please find the post you are referring to and press "quote". I looked back 20 or so posts and didn't see what you were talking about---could just be poor eyesight. If you find the post for me it will save me the effort of searching thru this lengthy thread for what you say is overbold. Thanks in advance.

I see you are a newcomer and want to extend an appreciative welcome, especially since not everyone here is as familiar with recent work on asymptotic safety. It's an interesting topic.

 

[arivero]

IMHO, discussion involving C-M is relevant, not deserving of ridicule, in the following sense...
The paper is titled "An Exceptionally Simple Theory of Everything". But there does not
seem to be a usable method to calculate scattering cross-sections. OK, C-M might not apply,

I agree, in a partial way: in a theory of everything with gravity, they should either have a G_Newton->0 limit, where scattering and C-M and all of QFT applies, or a way to show that the G_Newton->0 limit produces a trivial theory (for instance, that it also cancels all the other fields).
Similarly, they should have a gauge QFT ->0 limit, where only gravity survives, or a way to show that gauge->0 also cancels the gravity part.

In the case of triviality of the ->0 limits, a more complicated study is called for: large distances will emerge gravity only, short distances will emerge QFT only. It is more complicated because very short distances recall Planck length and thus gravity again.

 

[hch]

Here's the link to Bee's discussion
http://backreaction.blogspot.com/2007/11/theoretically-simple-exception-of.html

A point that comes out there, as I would interpret it, is that Garrett's "quantum E8 theory" requires a Lambda that is 16 orders of magnitude larger than observed but this could actually be a plus.

Bonanno Reuter's recent paper says Lambda true value, what it is at the UV FIXED POINT, before it runs down with decreasing energy and expanding scale, is in fact much larger than what we observe, and this, Bonanno Reuter say EXPLAINS INFLATION. Heh heh. They could be right!

Several of Reuter's papers say this, but here is the Bonanno and Reuter link, for one:
http://arxiv.org/abs/0706.0174

So assuming that's right, if you have a FUNDAMENTAL theory that determines a value of Lambda, then you want the determined fundamental value to be very large.

Apparently this idea is floating around and is shared by others besides the immediate Asymptotic Safety bunch. So we don't have to pin it on people like Percacci and Reuter if we don't want. But Garrett cites them lightly for some reason in his paper, so perhaps they have his blessing. An associate of Percacci, named Nesti, is mentioned in the acknowledgments.

I think it would be really great if some fundamental theory, like Garrett's, would peg the cosmological constant really high and in agreement with what shows up at the Asymptotic Safety people's fixed point. It would harmonize early inflation with late acceleration and make sense generally of the whole expansion history.

Here is Garrett's comment about the large Lambda, that he made a few minutes ago at Bee's blog:
http://backreaction.blogspot.com/2007/11/theoretically-simple-exception-of.html#c4837564169156800942

At 12:16 PM, November 07, 2007, Garrett said...

bee:

Yes, at first I considered the large value of the cosmological constant in this model to be a worrisome bug. But now this idea is in agreement with current theories of a large cosmological constant at high energy (ultraviolet fixed point) running to the tiny value we experience at low energies. So the bug now looks to be a feature...

as you are probably well aware, there is no shortage of theories that require lambda to be orders of magnitude above the observed value.

 

[marcus]

as you are probably well aware, there is no shortage of theories that require lambda to be orders of magnitude above the observed value.

Not sure what the point of your remark is. There are some estimates based on conventional QFT which are way off. Unlike Reuter's treatment, they would predict that we should observe Lambda many orders of magnitude different from what is actually observed.

A treatment using RG flow trajectories and a UV fixed point (running scale-dependent Lambda) is an altogether different framework. If you require the distinction to be made clear then we really do need a separate thread. Discussing it here would take us far off topic. Would you like to start one, or shall I start a thread for you so we can talk about it?

==================

I see you have quoted my post #12, that mentions Reuter and other work involving running cosmological constant, and allows for the possibility that the work could be right or wrong. I don't see anything that needs additional qualification.

 

[marcus]

The discussion at Bee's blog has broken the 200 comment mark.
My last comment there was #200, Aaron Bergman's was #201.
It's like a loud party.
http://backreaction.blogspot.com/2007/11/theoretically-simple-exception-of.html

the person who is really missing in that discussion is John Baez

very good physics ideas can bring about the invention or recognition of new mathematics
(more often the recognition of already invented, and realization of its role in understanding nature)

G.L. E8 ToE in my humble opinion will eventually require the recognition of a new type of spacetime manifold and a new type of connection.

It could be a spacetime manifold that is locally deSitter instead of locally Lorentz.
Or where the local geometry is graded (i.e. energyscale dependent)

I guess in the best and free-est discussion people should be free to speak carelessly off-cuff and not suffer the chilling effect of being quoted, but I very much liked an off-the-cuff exchanged between G.L and Bee, and want to quote the essentials.
Garrett said the E8 theory under construction was neither top down or bottom up but, instead, might be described as
"top-down inspired, bottom-up". My punctuation.
that is it is being built up by hand from the ground of the standard models----to match GR and particle SM---but there is an overriding mathematical idea that inspires it.

Bee said "what is the top that the inspiration comes down from?" or words to that effect. It is a really good and persistent question and it points to where mathematical creativity could play a role.

I think the idea of naturalness at the top---or which is inspiring the construction of the theory---is that geometry and matter are the same thing and should be described by the same mathematical object.

however classical geometry dynamics (GR) the geomtry was described by the metric, the distancefunction played the role of geometry.

Garrett pointed out at the seminar that a CONNECTION is just as good a way to represent the geometry and in some ways more NATURAL. he mentioned that one can recover a metric from a connection and a connection is a more elegant or economical way---it describes the spacetime manifold's shape by how things roll and twist as you truck them around on it. With a metric you have to figure out how to do transport, by studying distances. But the connection just tells you how, with less fuss and bother. That's its job.

So a connection is an inertial compass trucking dingus that covers the metric's job and the bonus is that it gives a natural way to describe FIELDS and their allowed interactions.

so the overriding math idea (from whence the inspiration for the bottom-up buiding work) is that geometry and matter are the same thing so let's try to describe them both with a connection dingus, and get a classical and eventually quantum dynamics of geometry and matter in terms of that.

And there is the question of WHAT KIND OF 4D SPACETIME MANIFOLD it should be built on (because there are various definitions of manifold available in differential geometry, and of course one can invent new ones) and then WHAT KIND OF CONNECTION on what kind of bundle. A bundle is where you plant a copy of E8 at each point of the manifold and then talk about connecting them up. E8 is the egg of the universe, it is what defines our world of interacting matter and geometry, so naturally you want a copy of it at each point because that describes each point of our world. The nontrivial part is connecting.

These are just my inexpert reactions as a spectator. What I am anticipating is that a real mathematician will show up and say something like----hmmm Garrett's E8 doesn't have Lorentz flat symmetry in it, it has deSitter, so we have to do something about the underlying manifold. It might have a curved tangent space. And also it looks like Lambda is energyscale-dependent, so the manifold might be scale-graded in some sense. It might need to be able to have a dimensionality that varies with scale---so that it becomes fractal-like and lower dimensiony at very small scale...

We have this odd thing that in nature space expands----but the flat Minkowski space of special relativity doesn't. To be fundamental it seems intuitive that a theory could not be built on a manifold that is locally Minkowski. More likely one that is locally deSitter...

but these are my hunches and they don't matter, I just want to indicate some of the room outside the box. If it turns out that the E8 theory has the potential to GROW mathematics, like feet that require a new size of shoes, so as not to mis-shapen their ToEs.

 

[gnocchi]

I've started Wikipedia pages for http://en.wikipedia.org/wiki/Garrett_Lisi" if anyone wants to add to them.

 

[arivero]

http://reddit.com/info/60msi/comments/
http://science.reddit.com/info/60n0z/comments/

The discussion at Bee's blog has broken the 200 comment mark.
My last comment there was #200, Aaron Bergman's was #201.

Is bee going to close at #240?

http://backreaction.blogspot.com/2007/11/theoretically-simple-exception-of.html
the person who is really missing in that discussion is John Baez

It seems that the traditional role of E8 as GUT group is not reviewed in detail, so perhaps the remarks of Tony here and there are enough. But yep, you are right, some remark of Baez feels lacking.

 

[AzMa]

Two Questions:
I recently stumbled on a comment made by kkenn on reddit that goes as follows: ""Stuns" in the sense of "Wha? How is this a theory of everything?"

From what I can see, he has proposed a way to rearrange the particle content of the standard model into representations of E_8. This is not new in concept, people do this all the time in grand unified theories.

The new part is that he is claiming that he can embed all of the particle content of the standard model plus gravity into E_8.

However, he does not yet have a full theory of the interactions (quantized Lagrangian) which can be studied and compared to existing predictions. Only once you have this is it reasonable to say you have "a theory". Up until this point, you just have some patterns that you have observed which might emerge from a theory.

Historical note: this happened in the 1960s in the development of QCD: Gell-Mann noticed that particles could be assembled into representations of SU(3); this was not itself a theory of the strong interactions, but it helped point the way to the development of one. So this approach is not new, and in fact theoretical physicists have been trying to apply it to grand unified theories for 4 decades.

However, in this case, in order to fit the representations together into E_8 he is doing some things which are, on the face of it, mathematically extremely dubious and should give serious doubt about whether the his formulae make any sense at all.

For example, his expressions combine bosons and fermions as if they can be simply added. But these fields have opposite statistics (commuting vs anti-commuting), so it makes no sense to just add them; the resulting mathematical object makes no sense. In blog comments he keeps pointing to BRST symmetry as an example of where physicists do this, but has not addressed the basic point that in BRST symmetry the fermions are "ghosts" with the wrong statistics, and there is a way to make mathematical sense of this case. This problem is well-known to other physicists working on grand unified theories, but here it is just avoided by assuming there is some kind of "formal" structure in which it makes sense.

This kind of confusion probably comes from being extremely imprecise about the definitions of various quantities that are being manipulated throughout the paper, and an attempt at notational simplicity (very few of his formulae are written with indices, which is OK as long as you are very careful to check that they make sense - leaving indices in makes expressions notationally more complex but is an easy consistency check that you are not doing something silly).

I suspect this is misleading him into writing expressions that fit the concepts that the author wants, but do not make mathematical sense as an expression of those concepts.

Another fundamental theorem (the Coleman-Mandula theorem) is also ignored by asserting that it does not apply (even though it must, in the regime where space is approximately flat). This theorem is a basic mathematical result that says that what the author is attempting is fundamentally not possible once he starts to introduce interactions between his fields, and to just wave it away like that is also quite disingenuous. Again, there is 4 decades of research into this theorem, and one should be extremely skeptical when an author claims it does not apply to them.

Some other problems (basically, all the hard problems of whether -- once the author actually has a theory that he can begin to calculate with -- it will match with the extremely precise data required of it) are swept under the rug with the assumption that they will magically work out once he actually has the full theory. At this stage he can perform no such calculations because there is no theory to calculate with."

Now I would love to know if this is actually reasonable criticism of the theory or if it's merely a load of BS from I guy who only thinks he know what he is talking about.

Secondly, does this new theory allow for other universes (as in a multiverse)?

*If these seem like incredibly stupid questions, I apologize. Other than the general concept, this stuff has always been way over my head (probably because I'm only a junior in high school). But of course, that doesn't mean I'm not interested.

 

[staf9]

Kind of a novice-ish question here:
With gravitational so(3,1), I'd assume we're using a Lorentzian manifold signature there. Is that assumption right? If so it couldn't be DeSitter. If we do describe the universe as locally DeSitter, I always believed that it could lead to a theory of faster-than-light travel (due to constant exponential inflation) which doesn't sound very plausible anyway.

One more thing, since the paper describes bosons and fermions which are being represented as Grassman valued fields, shouldn't we use some other form of Lie algebra instead of just a simple Lie algebra because of the Grassmans involved?

 

[CarlB]

The one thing I haven't seen mentioned here is that when physics finds nice pretty symmetries that explain the known particles, it seems that they end up replacing the idea with a theory of more elementary particles. The most recent time this occurred was with the quarks, which started out as an application of SU(3).

 

[jal]

Who is going to be able to show that the “other theories/models” fit into E8?
“They” won’t do the work it has to be done by an E8 team.
Here is what I found for a recent search of arxiv.org

http://arxiv.org/find/hep-ph/1/au:+Forkel_H/0/1/0/all/0/1
Holographic glueball structure
Authors: Hilmar Forkel
------------
http://arxiv.org/PS_cache/arxiv/pdf/0711/0711.2259v1.pdf
The Pion Cloud: Insights into Hadron Structure
Anthony W. Thomas
Jefferson Lab, 12000 Jefferson Ave., Newport News VA 23606 USA and
College of William and Mary, Williamsburg VA 23187 USA
14 Nov 2007
-------------
http://arxiv.org/PS_cache/arxiv/pdf/0711/0711.1703v1.pdf
Probing the nucleon structure with CLAS
Highlights of recent results.
Volker D. Burkert, for the CLAS collaboration.
Jefferson Lab, Newport News, Virginia, USA
November 12, 2007
----------
http://arxiv.org/PS_cache/arxiv/pdf/0711/0711.2048v1.pdf
Nucleon Structure from Lattice QCD
David Richards
Jefferson Laboratory, 12000 Jefferson Avenue, Newport News, VA 23606, USA
November 12, 2007

 

[garrett]

One more thing, since the paper describes bosons and fermions which are being represented as Grassman valued fields, shouldn't we use some other form of Lie algebra instead of just a simple Lie algebra because of the Grassmans involved?

The connection involves only Lie algebra valued 1-forms and Lie algebra valued Grassmann numbers. Nothing fancier.

 

[CarlB]

In Baez's paper on the octonions:
http://math.ucr.edu/home/baez/octonions/oct.pdf
which I think really needs to be read in conjunction with Garrett's, the most interesting description of $$E_8$$ to me is on page 48:

With 248 dimensions, $$E_8$$ is the biggest of the exceptional Lie groups, and in some ways the most mysterious. The easiest way to understand a group is to realize it as as symmetries of a structure one already understands. Of all the simple Lie groups, $$E_8$$ is the only one whose smallest nontrivial representation is the adjoint representation. This means that in the context of linear algebra, $$E_8$$ ismost simply described as the group of symmetries of its own Lie algebra!

In the usual state vector formalism of QM, this is just an interesting factoid. But if you represent quantum states in the density operator or density matrix formalism, it begins to make a little intuitive sense.

In the state vector formalism, states are represented by state vectors. These are operated upon by operators. In the density operator formalism, both the states and operators are operators.

Now if you define "quantum state" as a thing which is defined by its symmetry, and you also require a density operator formalism, then $$E_8$$ is the only choice if you demand that the same objects represent the quantum states and also the symmetries of the quantum states.

If you start with something smaller, it will have to grow. If you start with something larger, it will not be simple and it will have undetermined coefficients.

 

[marcus]

I'm concerned about simple question-answering fatigue. (Not on my part. I'm laid back and quite often let questions go for a day or two.)

the two that keep coming up, though answered by G.L. many times at Bee's, are
1)adding fermions and bosons
2) Colemandula

Abhay Ashtekar, the wise old Elephant of quantum gravity, has given us plenty with which to beat down the Colemandula objection if we just get up the gumption to do it.
He said it was a "completely different framework". He's smart and saw this right away.

But there are some string theorists who are slow to get it (like AzMa's kken on reddit, and like some at Bees blog). Read my lips, says Ashtekar: Colemandula does not apply here.

the other question I have the feeling CarlB could explain to me why 'tis not a problem.
I keep hearing about Z₂ graded algebras. That is a very simple mathematical idea, just a direct sum of two and a rule that when multiplying you add the grades mod 2.
I have this idea, please tell me if I am wrong, that it would ease things if only everyone in discussion was familiar with the idea of a Z₂ graded algebra. If I'm wrong, don't bother to explain why, just tell me I'm on the wrong tack.
===================

Ashtekar said another really wise thing at the seminar: "You have to solve problems one at a time."

I think that means that a theory is developed by successive approximations. If some facet looks almost right, you leave it for the moment and go fix something else. The next time round, with the next version, it's better and so on.
Something the present version seems to have in spades is predictivity. Instead of yelling all these reasons why they think the theory can't possibly work (which tend to be based on misunderstanding) you'd think we could all accept the fact that it MIGHT work and wait politely to see some of the predictions, which are surely going to be derived.

 

[Mephisto]

slightly off-topic,
an article about this theory was posted on digg today and generated a lot of buzz with almost 6000 diggs in 10 hours, which as a regular reader, I can tell you, is pretty rare and quite great; Especially considering that this is a highly technical subject. A direct link:
http://digg.com/general_sciences/Surfer_Dude_Stuns_Physicists_With_Theory_of_Everything_2

I'm only an undergrad in physics so I'm lost in the details, but I am really excited about your theory, and I hope you are right. Deriving laws of physics by geometric means like this seems really nice, elegant and strangely mysterious.

 

[christianjb]

Writing as someone who doesn't understand this paper at all:

The more I read about this work the more exciting it seems. I'd like to offer my congratulations to Lisi. It makes me happy to be a member of the human species when I see how imaginative we can be.

Even if this turns out to be wrong- it's inspiring to see scientists trying to find deep symmetries in physical law.

Lisi seems like a great guy and I hope his work continues to bring inspiration to others like me who can only gaze in awe at all of this.

 

[Ivan Seeking]

This is all very exciting!

Congratulations Garrett, and good luck!

[we may need to create a Big Kahuna medal... ]

 

[marcus]

[we may need to create a Big Kahuna medal... ]

Nice idea. i wonder what it would look like.
Another idea would be just turn on the avatar image option (as for an honorary so-and-so) and see what iconic device he devises.

 

[arivero]

slightly off-topic,
an article about this theory was posted on digg today and generated a lot of buzz with almost 6000 diggs in 10 hours, which as a regular reader, I can tell you, is pretty rare and quite great;

Yep, the reactions in digg, reddit (quoted some messagges before) and meneame are very curious. In any case, it proves that the people writing newspapers has some knowledge about what is going to connect with the public.

 

[arivero]

Slashdot reaction
http://science.slashdot.org/article.pl?sid=07/11/15/2322225&from=rss
seems to have better comments (partial impression, it can be) that the other popular forums. But what amazes me is (personal feel, again) that public seems not react about the personal character of Lisi, but about the fact that someone, nowadays, is still researching for unified, GUT or TOE theories.

 

[Coin]

Hi,

So the comments about Coleman-Mandula do seem to be causing some very repetitive discussion, but there is still one thing about that I would like to ask for a clarification on if that's okay. Garrett's position on Coleman-Mandula seems to be that Coleman-Mandula as originally formulated is based on conditions that do not apply to E8, specifically the presence of the poincare group as a subgroup, and that anyone who wants to claim Coleman-Mandula is true more generally than just the poincare group has the burden of proof of showing that to be true. Okay, that is fair. However in the Backreaction comments Tony Smith posted:

Steven Weinberg showed at pages 12-22 of his book The Quantum Theory of Fields, Vol. III (Cambridge 2000) that Coleman-Mandula is not restricted to the Poincare Group, but extends to the Conformal Group as well.

Since the Conformal Group SO(4,2) contains Garrett's de Sitter SO(4,1) as a subgroup, it seems to me that it is incorrect to claim that use of deSitter SO(4,1) means that Coleman-Mandula "... does not apply ..." to Garrett's E8 model.

That I have seen, there was not any response to or generally any notice of this. It seems to have been lost in the shuffle of comments.

Now, I honestly don't understand Coleman-Mandula, and I certainly don't know anything about Weinberg's claimed extension to the Conformal group cited here! (Although on the face of it I'm not quite sure it applies, it sounds like Weinberg would have proved that CM applies to anything which has SO(4,2) as a subgroup, but E8 doesn't have SO(4,2) as a subgroup, it only shares the subgroup SO(4,1) in common with SO(4,2)? Are the conditions met or not here?) But it seems to me that if Tony Smith is right then this is an important point. If Weinberg already did, as Garrett puts it, "prove the results of the Coleman-Mandula theorem while weakening condition (1)", then it seems to me there needs to be some response to that. Is there one?

 

[jal]

I want to make a comment on the success of this thread.

I hope that the regulars (here) have taken the time to look at the link from arivero Slashdot reaction
http://science.slashdot.org/article...22225&from=rss

and at the link from Mephisto

"... digg today and generated a lot of buzz with almost 6000 diggs in 10 hours, which as a regular reader, I can tell you, is pretty rare and quite great; Especially considering that this is a highly technical subject. A direct link:"
http://digg.com/general_sciences/Sur...Everyt hing_2
--------------
The interest is there ... the communication links are very weak.
and if YOU thought that I was making things toooo simple in my blog, think again.
-----------

 

[staf9]

Congratulations Garrett!

Thanks very much for staying involved in this thread and the backreaction one your answers are helping me (and many others I'd guess) understand this paper much more than we would have without

In addition:

... If Weinberg already did, as Garrett puts it, "prove the results of the Coleman-Mandula theorem while weakening condition (1)", then it seems to me there needs to be some response to that. Is there one?

Steve Weinberg's book, The Quantum Theory of Fields, Vol. III, was published in 2000, so I'm sure if you run a google search or do some forum hunting you can find some responses to his publication. I'll look around and repost here if I find anything.

Though maybe this quote from tony smith on backreaction may shine some light on things:

In short, since E8 is the sum of the adjoint representation and a half-spinor representation of Spin(16),
if Garrett builds his model with respect to Lorentz, spinor, etc representations based on Spin(16 consistently with Weinberg's work,
then
a beautiful aspect of Garrett's model is use of the fermionic and bosonic aspects of E8 so that Coleman-Mandula is satisfied.

Read some of Tony's other posts and Garrett's responses to them on backreaction, it should answer many of your questions.

Of course, with all this talk of the Coleman-Mandula thm, I don't know what this would bode for supersymmetry (though it is a Lie superalgebra instead of a Lie algebra).

 

[CarlB]

Okay, I've got my E8 root rotating Java applet up, enjoy:
http://www.measurementalgebra.com/E8.html

It starts up with a random rotating view of the roots, but you can change the parameters to give some other view. You can also change the colors of the individual roots.

There are 240 roots. I've listed the 112 $$so(16)$$ roots first, then the 128 $$16_{S+}$$. To change the color of them you would have to go through a lot of grief. I know, I'll be updating it with improvements as I go along.

The root structure shows how the fermions and bosons are kept separate. [edit] This is completely wrong, but a nice description of the roots anyway. I'm editing it to make it compatible with Lisi's particle assignments.[/edit]

The root vectors are 8 dimensional, that is, they are vectors of length 8. 128 of the roots carry quantum numbers of +-1/2, but there are an even number of +s (and therefore an even number of -s too). A typical root vector (set of 8 quantum numbers) is:

(+0.5, -0.5, -0.5, -0.5, +0.5, -0.5, +0.5, +0.5)

Note that the above has 4 - signs and 4 + signs. Since "4" is an even number, this is a legal fermion vector. The other 112 roots are defined by the minimal changes between these first 128. That is, define a distance function on the roots given by the sum of squares of the differences between the roots. The first 128 have even numbers of +s and -s, so this means that two roots have to change. The change is from +1/2 to -1/2 or back. Thus the other 112 roots are all the ways of choosing two quantum numbers out of 8, with those two quantum numbers being +1 or -1independently.

For example, here are two of the first 128 roots that are separated by the minimal distance:

(+0.5, -0.5, -0.5, -0.5, +0.5, -0.5, +0.5, +0.5)
(+0.5, +0.5, -0.5, +0.5, +0.5, -0.5, +0.5, +0.5)

The difference between them is a typical element from the last 112 roots:

(0.0,+1.0, 0.0, +1.0, 0.0, 0.0, 0.0, 0.0)

These last 112 roots have two non zero elements. But they can be positive or negative. And they can be anywhere in the vector. Another typical case:

(0.0,-1.0, 0.0, 0.0, 0.0, 0.0, +1.0, 0.0)


This has preon model written all over it. More later.