An Exceptionally Simple Theory of Everything! [Archive]

jal

Nov7-07, 08:34 AM

The theory proposed in this paper represents a comprehensive unification program, describing all fields of the standard model and gravity as parts of a uniquely beautiful mathematical structure. The principal bundle connection and its curvature describe how the E8 manifold twists and turns over spacetime, reproducing all known fields and dynamics through pure geometry. Some aspects of this theory are not yet completely understood, and until they are it should be treated with appropriate skepticism. However, the current match to the standard model and gravity is very good. Future work will either strengthen the correlation to known physics and produce successful predictions for the LHC, or the theory will encounter a fatal contradiction with nature. The lack of extraneous structures and free parameters ensures testable predictions, so it will either succeed or fail spectacularly. If E8 theory is fully successful as a theory of everything, our universe is an exceptionally beautiful shape.
Acknowledgments
The author wishes to thank Peter Woit, Sergei Winitzki, Lee Smolin, Tony Smith, David
Richter, Fabrizio Nesti, Sabine Hossenfelder, Laurent Freidel, David Finkelstein, Michael
Edwards, James Bjorken, Sundance Bilson-Thompson, John Baez, and Stephon Alexander for valuable discussions and encouragement.

I am remembering the work done by Chris Quigg and The Double Simplex http://arxiv.org/find/hep-ph/1/au:+Quigg_C/0/1/0/all/0/1 and the work done by Tony Smith http://www.valdostamuseum.org/hamsmith/goodnewsbadnews.html

Your work is only beginning.
Good luck Garrett! With the availabilities of the new computer programs, you should be able to communicate this model better than your predecessors.

marcus

Nov7-07, 08:35 AM

Garrett, two questions

To derive predictions will it be necessary to do awesome numeric feats like computing E8 10j symbols? (I know you said you had a few more things to understand before discussing this so it probably is not a fair question.) Or will there be some relativity cheap easy predictions and if so what might they look like?

You mentioned a handful of unobserved particles. Where, in the article, are they listed? Can one speculate anything about what they might be like? Could they be candidates for solving any of the outstanding comic puzzles? [sic]

And the third question, of course, is will you be snowboarding in the Sierras this winter?

ccdantas

Nov7-07, 09:29 AM

Congratulations to Garrett, it's a beautiful paper and it's science. It can be right or wrong.

Bee over at her blog makes some considerations on it.

I wish Garrett all the best with his work!

Christine

ccdantas

Nov7-07, 09:40 AM

And BTW I would attempt those computer calculations myself with the machinery available here, if I only knew how to do them! I'd need some time to understand Garrett's work in order to build up the programs, etc. I suppose one would need to run the calculations in a high performance computing environment (e.g., a beowulf cluster).

Christine

garrett

Nov7-07, 10:09 AM

To derive predictions will it be necessary to do awesome numeric feats like computing E8 10j symbols? (I know you said you had a few more things to understand before discussing this so it probably is not a fair question.) Or will there be some relativity cheap easy predictions and if so what might they look like?

I think burly spin network calculations will only be necessary for figuring out what's going on down at the Planck scale. Standard QFT should be suitable for figuring out how couplings and masses run at lower energies. Predictions... there are twenty or so constants in the standard model I've got my eye on...

This is an "all or nothing" kind of theory -- meaning it's going to end up agreeing with and predicting damn near everything, or it's wrong. At this stage of development, it could go either way.

You mentioned a handful of unobserved particles. Where, in the article, are they listed? Can one speculate anything about what they might be like? Could they be candidates for solving any of the outstanding comic puzzles?

Sure, I talk about them on pages 21 and 22. They're weakly interacting colored scalar fields. These seem like a decent dark matter candidate. But, as I said, this theory is still under development and I can't currently make predictions with any confidence.

I published the paper because things were beginning to look too good to just keep working on it on my own.

And the third question, of course, is will you be snowboarding in the Sierras this winter?

Three times a week, starting as soon as we get some snow. And I brought some kites over from Maui too, so I'm looking forward to trying some kite-snowboarding. :)

garrett

Nov7-07, 10:14 AM

I am remembering the work done by Chris Quigg and The Double Simplex http://arxiv.org/find/hep-ph/1/au:+Quigg_C/0/1/0/all/0/1 and the work done by Tony Smith http://www.valdostamuseum.org/hamsmith/goodnewsbadnews.html

Your work is only beginning.
Good luck Garrett! With the availabilities of the new computer programs, you should be able to communicate this model better than your predecessors.

Thanks, jal. I think Tony has a lot of things right, and I got a lot of good hints from his stuff. I hadn't seen Chris Quigg's work -- it looks interesting and I'll bet it matches up with E8 in a lot of ways.

garrett

Nov7-07, 10:22 AM

Bee over at her blog makes some considerations on it.
I wish Garrett all the best with his work!

Thanks Christine. Sabine has written a very nice overview.

And BTW I would attempt those computer calculations myself with the machinery available here, if I only knew how to do them! I'd need some time to understand Garrett's work in order to build up the programs, etc. I suppose one would need to run the calculations in a high performance computing environment (e.g., a beowulf cluster).

I use Mathematica a lot, running on my mac. I nearly melted a hole in my dining room table running the calculations to produce this movie:

http://deferentialgeometry.org/anim/e8rotation.mov

High powered computing isn't necessary for playing with the basics.

marcus

Nov7-07, 11:53 AM

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 acknowledgements.

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...

shoehorn

Nov7-07, 01:13 PM

In the interests of balance, we should probably point out that Lubos has savaged the paper.

garrett

Nov7-07, 02:01 PM

Lubos' post is a hoot!

First he makes two statements that are blatantly wrong, and uses these to justify saying there's no physics in the paper. Then he attacks the physics in the paper. Heh.

His only rational attack is based on the Coleman-Mandula theorem, the abstract of which he kindly provides a link to, but evidently didn't read, since the first assumption of the C-M theorem is stated there in the abstract, and doesn't apply in the case at hand, as stated in the paper. The only other arguments he employs are ad hominem, based on my association with other non-string researchers who I am proud to call colleagues.

I couldn't have asked Lubos to write a more helpful critique, as it fails in its goal of tearing down the paper, while confirming just how different this E8 theory is from string theory.

jal

Nov7-07, 04:00 PM

3. Dynamics
... In any case, the dynamics depends on the action, and the action depends on the curvature of the connection.
Huuummmm!!!...Can I assume that your are saying that the structure (E8) is scale independent?
The scale would come from the inputs?
jal

Hans de Vries

Nov7-07, 04:01 PM

Hi, Garrett.

I just wonder if you had any considerations concerning your quark
related matrix (2.4)

\left(\begin{array}{ccc}
-\sqrt{1/3},& -\sqrt{1/3}, & -\sqrt{1/3} \\
-\sqrt{1/2},& +\sqrt{1/2}, & 0 \\
-\sqrt{1/6},&-\sqrt{1/6},& \sqrt{2/3}
\end{array}\right)

and the tribimaximal matrix for neutrino mixing? see here (eq:4)

http://arxiv.org/PS_cache/hep-ph/pdf/0606/0606024v1.pdf

Which can be written as a tetrahedral symmetry:

\left(\begin{array}{ccc}
z_1,& y_1,& x_1\\
z_2,& y_2,& x_2\\
z_3,& y_3,& x_3
\end{array}\right)\ =\
\left(\begin{array}{ccc}
\sqrt{1/3},& \sqrt{2/3},& 0\\
\sqrt{1/3},& -\sqrt{1/6},& +\sqrt{1/2}\\
\sqrt{1/3},& -\sqrt{1/6},& -\sqrt{1/2}
\end{array}\right)

They are the same except for a transpose, a coordinate swap
and a mirror operation. see also the other links here
http://www.physicsforums.com/showthread.php?p=1496398#post1496398

Regards, Hans

garrett

Nov7-07, 05:25 PM

Hi Hans,

Yes, Carl just pointed this out for me earlier today. The transpose and coordinate swap are easy to accommodate -- it's the same matrix, geometrically. This matrix rotates a cube such that two opposing corners line up on an axis. In the paper I'm using it to embed the su(3) root system in a so(6) subalgebra of E8. The fact that this "tribimaximal matrix" may relate neutrino masses is fascinating! It will almost certainly play a role as this E8 theory develops -- this matrix is used in conjunction with a triality rotation between generations.

All along, while working on this stuff, my feeling grew stronger that this theory is much too large for me to work on alone. There are pieces, like this one, that will fit in ways I didn't even know about. I'm very happy now that others are also excited about it and working with these ideas.

garrett

Nov7-07, 05:41 PM

Huuummmm!!!...Can I assume that your are saying that the structure (E8) is scale independent?
The scale would come from the inputs?

I'm not sure what you mean by "inputs."

jal

Nov7-07, 06:23 PM

I should have specified/said "minimum length".

garrett

Nov7-07, 08:03 PM

I should have specified/said "minimum length".

Ah, OK. I don't have anything to say about a minimum length.

CarlB

Nov7-07, 11:51 PM

In the paper I'm using it to embed the su(3) root system in a so(6) subalgebra of E8.

This helped a lot, and explains a lot. I still haven't had time to gather together your paper, head phones, rock and roll CDs, and 4 to 6 hours. But I will probably have more questions.

While I was driving back from a meeting with the Fire Marshall at Moses Lake, Washington, I was thinking about why that particular choice of orthnormal rotation came about.

The (1,1,1) axis is pretty obvious. It's an axis around which everything has a nice 120 degree rotation.

But after you make that choice you still have another choice to make and it's not entirely obvious to me why there should be some content in how it is made. I guess one puts a zero in one of the remaining 6 entries and you get the tribimaximal matrix.

The (1,1,1) axis amounts to a scalar, and the other two are a two element vector of some sort I guess. What I don't get is how one chooses the particular angle to get the tribimaximal matrix. I guess this amounts to the same thing as "how do you break symmetry".

P.S. The other problem is getting the Koide rotation angle of 2/9. I blogged my guess for where the angle comes from here:
http://carlbrannen.wordpress.com/2007/09/22/infrared-correction-to-mass-i/

but I haven't finished the nasty calculation.

CarlB

Nov8-07, 12:00 AM

Lubos' post is a hoot!

From my point of view, the error in Lubos' analysis is that he is assuming that the underlying structure is the usual spin structure that comes from special relativity. In that kind of a structure, the left and right halves of a particle have to appear together.

On the other hand, what I think you're doing (and what I'm pretty sure I'm attempting) is to describe the handed states individually, and then stitch them together with a mass interaction.

If you do it that way, there is nothing particularly nasty about putting singlets and vectors into the same representation. It's a matter of how the mass interaction adds the spin structure to the otherwise separate states. In fact, without that kind of thing, you inevitably end up with arbitrary parameters.

garrett

Nov8-07, 12:32 AM

This helped a lot, and explains a lot. I still haven't had time to gather together your paper, head phones, rock and roll CDs, and 4 to 6 hours. But I will probably have more questions.

Cool.

The (1,1,1) axis is pretty obvious. It's an axis around which everything has a nice 120 degree rotation.

Yes, that's called a triality rotation.

This matrix is a rotation matrix that takes the (1,1,1) axis to (1,0,0) (or something like it). After this rotation, rotations of 120 degrees around (1,0,0) are a symmetry of the cubic lattice. ( It's all about the cube (http://www.timecube.com/) :wink: )

From my point of view, the error in Lubos' analysis is that he is assuming that the underlying structure is the usual spin structure that comes from special relativity. In that kind of a structure, the left and right halves of a particle have to appear together.

Yes, I think you're right about this. I'd try to set him straight, but it's more entertaining to have him call me a crackpot. After all, one is reflected by their critics, as well as their supporters.

On the other hand, what I think you're doing (and what I'm pretty sure I'm attempting) is to describe the handed states individually, and then stitch them together with a mass interaction.

Exactly so.

If you do it that way, there is nothing particularly nasty about putting singlets and vectors into the same representation. It's a matter of how the mass interaction adds the spin structure to the otherwise separate states. In fact, without that kind of thing, you inevitably end up with arbitrary parameters.

Yes, it would be nice to derive the CKM and PMNS matrices from geometry and QFT.

jal

Nov8-07, 09:41 AM

There are too few people who take the time to discuss their paper in a blog or here. I see that you are trying to do both places.
Thanks!
I cannot ask questions at the level of CarlB so if you want to put up with me I would like to ask different questions.
The first observation/question that I have is that E8 structure exist whether the positions are occupied or not?
Therefore, I visualize/conclude that if you rotate a certain way you would get/see a proton.
Rotate another way and you would get/see a neutron.
Rotate another way and you would get/see dark energy.
Rotate another way or remove the “particles” and you get/see ... ??? the spacetime structure.

I'll try to explain your answer to grandma.
jal

arivero

Nov8-07, 09:48 AM

From my point of view, the error in Lubos' analysis is that he is assuming that the underlying structure is the usual spin structure that comes from special relativity. In that kind of a structure, the left and right halves of a particle have to appear together.

Lubos criticism is not very constructive. A better question had been about uniqueness, ie for which groups, besides the standard model group, can the structure of Lisi be built.

arivero

Nov8-07, 09:51 AM

I'll try to explain your answer to grandma.
jal

Try to explain your answer so that grandpa can understand it.

(Apocryphal, or course...)

garrett

Nov8-07, 11:31 AM

There are too few people who take the time to discuss their paper in a blog or here. I see that you are trying to do both places.
Thanks!

You're welcome. I love this stuff, and enjoy talking about it.

The first observation/question that I have is that E8 structure exist whether the positions are occupied or not?
Therefore, I visualize/conclude that if you rotate a certain way you would get/see a proton.
Rotate another way and you would get/see a neutron.
Rotate another way and you would get/see dark energy.
Rotate another way or remove the “particles” and you get/see ... ??? the spacetime structure.

I'm not exactly sure what you mean. But the pretty plots, which you can show to grandma, are projections of all the E8 Lie algebra elements (corresponding to roots in eight dimensions) that show the pattern of interactions for the various particles of the standard model. These patterns are there in E8, all I've done is label them with particle names.

garrett

Nov8-07, 11:34 AM

Lubos criticism is not very constructive. A better question had been about uniqueness, ie for which groups, besides the standard model group, can the structure of Lisi be built.

Yes, this is a good question. I have broken the E8 symmetry in a very specific way to get the standard model. I suspect there are many other ways to break the symmetry, and don't know yet why the standard model one might be chosen by nature.

marcus

Nov8-07, 11:35 AM

for readers who also like to follow the conversation between Bee, Moshe, and Garrett at Bee's blog, there are two especially interesting recent comments

Here Bee gives her own paraphrase of Garrett's approach, how she sees it and what aspects she sees as needing work
http://backreaction.blogspot.com/2007/11/theoretically-simple-exception-of.html#c8600779739364980235

She posted that about an hour ago, and Garrett replied a few minutes later filling some further explanation.
http://backreaction.blogspot.com/2007/11/theoretically-simple-exception-of.html#c4395346556977145096

a two-minds dialog is a good way of explicating something because you get whatever it is understood from two directions, I guess this was noticed by Galileo who was a kind of Renaissance blogger anyway and could whistle and chew gum at the same time (Galileo wrote dialogs not unlike what you find flashes of in blog comment sections)

Does anybody think it matters that Garrett's E8 model of existence is ALREADY predictive? It is already exposed to risk of falsification by LHC, unless I am missing something. finding evidence of SUSY would refute E8 and I don't see how it could accommodate extra space dimensions either. There is very little slack in the model.

jal

Nov8-07, 11:51 AM

yes! I'm jumping back and forth. Bee must have a good organizational team to have time to comment in her blog.
I've got an image in my mind that I'll keep for now since it's probably wrong. Maybe another image will come from reading the posts.
jal

jal

Nov9-07, 09:56 AM

Hi garrett

I've been following what has been discussed at Bee's blog.
As I expected, you and tony left me behind.

I'm not exactly sure what you mean. But the pretty plots, which you can show to grandma, are projections of all the E8 Lie algebra elements (corresponding to roots in eight dimensions) that show the pattern of interactions for the various particles of the standard model. These patterns are there in E8, all I've done is label them with particle names.
The dance floor is too full.
I hope that eventually you will be able to reduce the patterns (3D) to make it possible to explain to grandma.
jal

garrett

Nov9-07, 10:20 AM

The dance floor is too full.
I hope that eventually you will be able to reduce the patterns (3D) to make it possible to explain to grandma.

I suggest starting with the dance of the quarks and gluons in G2.

marcus

Nov9-07, 02:20 PM

as someone who navigates partly by hunches---touch and smell even--- I got a good feeling from this comment by Garrett at Bee's
http://backreaction.blogspot.com/2007/11/theoretically-simple-exception-of.html#c8778500176714763161

Please don't take my word for it. The first person I know of to point out this loophole in Coleman-Mandula was Thomas Love in his 1987 dissertation. There is also a discussion of this loophole in this recent paper by F. Nesti and R. Percacci: Graviweak Unification. Or you can go to the source and look at Coleman and Mandula's paper, in which their condition (1) for the theorem is "G contains a subgroup locally isomorphic to the Poincare group." The G = E8 I am using does not contain a subgroup locally isomorphic to the Poincare group, it contains the subgroup SO(4,1) -- the symmetry group of deSitter spacetime.

always a good sign when the deSitter group shows up instead of the Poincaré, after all the universe is expanding.

Derek Wise thesis was about understanding Mac-Mans gravity. I wonder if he is reading Garrett's paper at this point.

What kind of coalition will form around Garrett's gambit? Research is a relay race and maybe this paper defines a starting line. Sorry about incoherence. Maybe lunch would be a good idea.

CarlB

Nov9-07, 02:38 PM

What kind of coalition will form around Garrett's gambit?

Well, the empire has struck back, and the paper has been reassigned from physics/hep-th to physics/general. I don't think that will make much of an impression as far as the importance of the paper, but when you mess around with Poincare invariance it does tend to p:ss off the elders.

marcus

Nov9-07, 02:50 PM

Well, the empire has struck back, and the paper has been reassigned from physics/hep-th to physics/general. I don't think that will make much of an impression as far as the importance of the paper, but when you mess around with Poincare invariance it does tend to p:ss off the elders.

That was beautifully expressed, from beginning "Well..." to the final word.
I had read the news at Bee's blog, where it was brought by just the right messenger with just the right air of satisfied outrage and hysteria.
I expect a statement by Jacques Distler on "musings" which will justify the arxiv action without explicitly taking responsibility, before long.

He may have been already commenting at Bee's, as that particularly stubborn anonymous

Jim Kata

Nov9-07, 03:04 PM

Thankfully, I'm not afraid of looking ignorant

My knowledge of representation theory and octonions is very limited and definately not up to snuff to understand all of this paper like taking a real non compact representation of e8 but the thing I find the most interesting is triality.

Another thing is like, Hans and Carl pointed out, the possible connection between tribimaximal matrix and the matrix Garrett uses to embed the su(3) root system into so(6).

I have two questions one is off the wall and one is??

1.) The matrix in Garrett's paper, as he says, can be viewed as the twelve midpoints of the edges of a cube. Now I was not really thinking, but there are 12 leptons, and flavours of quarks, four for each generation. Do these midpoints on the edges of this cube represent each of the generations of quarks and leptons? I wish I could draw what I mean.

2.) Looking at figure 5 this theory seems to predict right handed leptons. Is this true? If so, is there a mechanism to explain why these are not observed?

marcus

Nov9-07, 03:23 PM

Peter Woit blogged Garrett's paper
http://www.math.columbia.edu/~woit/wordpress/?p=617
as well he might :smile:
as for the arxiv gnomes reclassifying the paper from hep-th to gen, fill in the consonants
_acques _ucques.
It's infuriating and depressing that someone at arxiv would stoop to something that dishonorable.

For this reason, and for its merits, I hope we choose this paper as our PF "Beyond" forum Paper of the Year.
It is a small thing but we should have some way, even a small symbolic one, of fighting back.

jal

Nov10-07, 12:55 PM

I see that garrett is carrying on simultaneous conversations in at least 3 places.
I have an observation that might help the beginners.
----------
Is there anyone out there capable of reading a knitting pattern?
You need to know the symbols for each action of the needles and when you apply that action a pattern will emerge.
The needles are flying off into the 3rd dimension and picking up the threads and leaving the threads in a 2d pattern.
There are moves that cannot be done.
Talk to a grandma.
E8 is a template for a knitting pattern. The pattern exists in our perceived 3d.
CERN will be able to look for the patterns that exist from 10^-15 to 10^-18. It will not be able to see the movement of the “needle” doing its dance that created the pattern. LQG will be needed to find out what the “needles” are doing.
I cannot knit, I cannot do LQG and much less E8.
However, if you succeed in writing the knitting pattern, grandma will be able to knit it.
----------
Ref.:
Proton
Mass m = 1.00727646688 ± 0.00000000013 u
Mass m = 938.27203 ± 0.00008 MeV [
Charge radius = 0.875 ± 0.007 fm
(diameter of about 1.6 to 1.7×10−15 m [1], and a mass of 938.27231(28) MeV/c2 (1.6726 × 10−27 kg), 1.007 276 466 88(13) u)
Mean life τ >10^31 to 10^33 years

marcus

Nov11-07, 06:28 PM

Garrett, want to clarify about the dimension? (for the not too smart spectator)
Baez when he talks about E8 says dimension 248
but I add 222 and 18 and get 240. So I am off by eight.

Just on a general level here is a paragraph on page 27 that I like a whole lot, and any comment or amplification from you would be welcome:

It should be emphasized that the connection (3.1) comprises all fields over the four dimensional base manifold. There are no other fields required to match the fieelds of the standard model and gravity. The gravitational metric and connection have been supplanted by the frame and spin connection parts of A.

The Riemannian geometry of general relativity has been subsumed by principal bundle geometry---a significant mathematical unification.

Devotees of geometry should not despair at this development, as principal bundle geometry is even more natural than Riemannian geometry. A principal bundle with connection can be described purely in terms of a mapping between tangent vector fields (diffeomorphisms) on a manifold, without the ab initio introduction of a metric.

these 8 missing dimensions, in my bad arithmetic, are they the "frame and spin connection parts of A" referred to above---or what, in simple terms, happened to them?

Hey people! Just by the way without the ab initio introduction of a metric means background independent. :biggrin: We are talking about background independent QFT which was, I guess, the whole idea in the first place. It's not surprising if some people are looking pretty happy at this point.

garrett

Nov11-07, 06:46 PM

Hi marcus,

The other eight Lie algebra elements are the basis elements of the Cartan subalgebra, so they're technically not included with the other roots. They are physical fields though -- six of them are standard and two are new.

With that paragraph you quote, I was saying something I think is important, but might not be widely known by physicists. Conventional GR requires a metric to exist over the manifold -- this is kind of a strange object from the point of view of differential geometry. Nevertheless, physicists are used to thinking of GR as geometric and Yang-Mills as involving algebra. However, Lie algebra elements correspond to vector fields over the Lie group manifold. And a principal bundle can be described purely in terms of maps between vector fields, without a metric, using a tangent vector valued 1-form field over the entire space. In this way, the geometry of principal bundles is more natural than Riemmannian geometry. But this is a very subtle point, and I don't expect it to mean much to most readers.

strangerep

Nov11-07, 09:00 PM

[Lubos's] only rational attack is based on the Coleman-Mandula theorem, the abstract of which he kindly provides a link to, but evidently didn't read, since the first assumption of the C-M theorem is stated there in the abstract, and doesn't apply in the case at hand, as stated in the paper.

Hi Garrett,

I don't understand the details of your dismissal of the C-M theorem. IIUC, you're basically
saying that it doesn't apply because in your setup we have deSitter instead of Poincare
(right?).

If so, then here's the thing that seems strange to me: deSitter contracts to Poincare
(for \lambda\to 0). Contraction is process of continuously changing the
structure constants. Pretty much everything else about the Coleman-Mandula theorem
seems to respect some form of continuity (analytic S-matrix, use of infinitesimal generators, etc).
So if you're relying on deSitter, then shouldn't we get negligible scattering unless
\lambda is significant?

Or am I naively expecting too much from continuity?

garrett

Nov11-07, 09:40 PM

Strangerep, you have hit the nail on the head. This E8 Theory, which includes MacDowell-Mansouri gravity as an integral part, is not defined for \Lambda=0.

Haelfix

Nov11-07, 10:38 PM

I was the anonymous person who brought up CM in Bee's thread.

And im still a little disturbed by it. Desitter space has no Smatrix, and if the action perse (MM) explicitly forbids contraction to regimes where CM applies, I can't see how you will recover the effective standard model field theory.

Read there is no apparent Smatrix in the theory!

Moreover even if there exists such a thing in the theory, I dont see how you will suppress unitarity violating interactions absent imposing a hard cutoff that generates gauge anomalies b/c it breaks the Desitter group. You need to run a general operator analysis to sort the mess out.

The topological sector of your theory is highly nontrivial as well, and I can't see how you will suppress all sorts of very bad instanton processes.

garrett

Nov11-07, 11:28 PM

I was the anonymous person who brought up CM in Bee's thread.

That's fine, it's certainly not a stupid question.

And im still a little disturbed by it. Desitter space has no Smatrix, and if the action perse (MM) explicitly forbids contraction to regimes where CM applies, I can't see how you will recover the effective standard model field theory.

It's going to have to be an approximation.

Moreover even if there exists such a thing in the theory, I dont see how you will suppress unitarity violating interactions absent imposing a hard cutoff that generates gauge anomalies b/c it breaks the Desitter group. You need to run a general operator analysis to sort the mess out.

The topological sector of your theory is highly nontrivial as well, and I can't see how you will suppress all sorts of very bad instanton processes.

Why do you think I published the paper? I can't do everything myself. :wink:

And I'm first to admit this is just the beginning of a theory that might be wrong.

Haelfix

Nov12-07, 02:45 AM

Don't get me wrong, thats fine. I happen to love E8 anyway, its a beautiful group

marcus

Nov12-07, 08:30 AM

I was the anonymous person who brought up CM in Bee's thread. .

It would be great to have more discussion about Coleman-Mandula. On Bee's thread the first mention I could find was Moshe around noon pacific on the 7th
http://backreaction.blogspot.com/2007/11/theoretically-simple-exception-of.html#c978188498139402984

At 12:38 PM, November 07, 2007, Moshe said...

Two quick questions:

1. What is the loophole in the Coleman-Mandula theorem used in this construction? note that the theorem allows constructing theories where internal and spacetime symmetries are unified, as long as those theories are free.

2. When packaging bosons and fermions together, at least one set of fields will have the wrong spin statistics relation. In addition to violating unitarity etc., this definitely is not what is going on in the standard model.

It led to quite a bit of discussion, some of which was echoed a couple of days later over at Peter's
==quote Woit's blog==
# more questions Says:
November 9th, 2007 at 6:57 pm

As long as Coin is asking questions, I didn’t understand (1) why this doesn’t violate the Coleman-Mandula theorem, and, (2) what about the nonrenormalizability of GR?

----

# Coin Says:
November 9th, 2007 at 7:24 pm

MQ, Garrett does seem to offer an argument concerning your (1) in a reply to Moshe in the comments section of the Backreaction post:

1. Yes, the Coleman-Mandula theorem assumes a background spacetime with Poincare symmetry, but this theory doesn’t have this background spacetime — with a cosmological constant, the vacuum spacetime is deSitter. So this theory avoids one of the necessary assumptions of the theorem, and is able to unify gravity with the other gauge fields. On small scales though, Poincare symmetry is a good approximation, and on those scales gravity and the other gauge feels are separate, in accordance with the theorem. (I’m not the first person to dodge C-M this way.)

Several more posts over the course of that thread drill down on this point further…

---

# Garrett Says:
November 9th, 2007 at 7:26 pm

more questions:

(1) The first person I know of to point out this loophole in Coleman-Mandula was Thomas Love (a visitor here) in his 1987 dissertation. There is also a discussion of this loophole in this recent paper by F. Nesti and R. Percacci: Graviweak Unification. Or you can go to the source and look at Coleman and Mandula’s paper, in which their first condition for the theorem is “G contains a subgroup locally isomorphic to the Poincare group.” The G = E8 I am using does not contain a subgroup locally isomorphic to the Poincare group, it contains the subgroup SO(4,1) — the symmetry group of de Sitter spacetime.

(2) I’m banking on the LQG community to crack this one. So multiply the odds of this E8 Theory being right times the odds of LQG finding the right answers for quantizing the theory… and I’m first to admit it’s a long shot. But I think it’s got a chance, which is why I work on it.
==endquote==

In his reply Garrett gives links for the Percacci-Nesti paper and for the Coleman-Mandula one.
I for one could use any further discussion of Coleman-Mandula that comes along and what especially interests me is that John Baez spent several weeks here at Beyond forum convincing us that the right local symmetry group for quantum field theory was SO(4,1) and not the Poincaré.
And I was convinced. So when people sound as if they think Garrett is fudging by using the deSitter group as an inferior substitute---to dodge the C-M no-go obstacle---then I wonder because it seems to me the reverse. It is the older work which uses the inferior substitute and this new work uses the RIGHT local symmetry.
And Colemandula be damned. If this is dumb, please help me see why.

jal

Nov12-07, 11:22 AM

I want to bring your attention to a drawing.
http://www.physicsforums.com/attachment.php?attachmentid=11509&d=1194846037
posted by Hans de Vries at

http://www.physicsforums.com/showthread.php?p=1501369#post1501369

If you do the same thing for E8, the shadow of the 3d construction produces the familiar E8 pictures.
A search, using “image”, will find it.
-------------
The 3d construction, if orientated properly, produces the tetras.
The hard question ….
Since a 3D construction of E8 can produce the 2D construction, What is the obstacle to assuming that the E8 is a construction existing in 3D?

garrett

Nov12-07, 01:02 PM

E8 lives in 8D. Sure, it can be projected down to 3D. It then needs to be projected to 2D to be shown on a screen or paper. If we used holograms instead of screens, I'd be making tons of 3D plots. But, as it is, I just project from 8D to 2D, because if I go from 8D to 3D to 2D, the perspective would make a mess of things.

Hans de Vries

Nov12-07, 02:01 PM

I want to bring your attention to a drawing.
http://www.physicsforums.com/attachment.php?attachmentid=11509&d=1194846037
posted by Hans de Vries at

http://www.physicsforums.com/showthread.php?p=1501369#post1501369

That image was generated with the (freeware) ray-tracer Povray.
All the projections come for free :smile: It's just setting up three light
sources on the principle orthogonal axis.

So the projections are actually shadows. You can give them colors as
I did by using transparent colored objects and/or colored light sources.

Regards, Hans

Hans de Vries

Nov12-07, 02:01 PM

It would be great to have more discussion about Coleman-Mandula.

Indeed, Theorems like that of Coleman and Mandula could be in
the same league as Lorentz invariance and Gauge invariance, with
respect to the guidance they can bring.

Weinberg handles the proof in appendix B of the first chapter (ch:24)
in Volume III handling the possible internal symmetries in combination
with the Poincaré group. Haven't studied the proof though ...

I don't think you can really "circumvent" Coleman Mandela by going
to another space-time group. You'll have to deal with the appropiate
version of the theorem for that specific group instead. I don't know
if there exist something along that line for SO(4,1). Weinberg refers
to chapter 32, the last chapter in Vol.III, for the application of
Coleman Mandela to higher dimensional spaces and he mentions
p-brane theories where the Theorem "does not apply"

Regards, Hans

CarlB

Nov12-07, 02:10 PM

With that paragraph you quote, I was saying something I think is important, but might not be widely known by physicists. Conventional GR requires a metric to exist over the manifold -- this is kind of a strange object from the point of view of differential geometry. Nevertheless, physicists are used to thinking of GR as geometric and Yang-Mills as involving algebra. However, Lie algebra elements correspond to vector fields over the Lie group manifold. And a principal bundle can be described purely in terms of maps between vector fields, without a metric, using a tangent vector valued 1-form field over the entire space. In this way, the geometry of principal bundles is more natural than Riemmannian geometry. But this is a very subtle point, and I don't expect it to mean much to most readers.

Is this referring to the work by the Cambridge geometry group?

http://www.mrao.cam.ac.uk/~clifford/publications/abstracts/gravity.html

garrett

Nov12-07, 02:35 PM

No Carl, you're not that lucky. :wink: I was referencing this:

http://deferentialgeometry.org/#%5B%5BEhresmann%20principal%20bundle%20connection %5D%5D
http://en.wikipedia.org/wiki/Ehresmann_connection

garrett

Nov12-07, 02:41 PM

CarlB

Nov12-07, 03:21 PM

This windows machine displays the Acrobat file beautifully. It makes a good addition to the arXiv article. It used to be my experience that very large Acrobat files (the above is 1.8MB) should be downloaded rather than opened directly.

Hans de Vries

Nov12-07, 03:37 PM

garrett

Nov12-07, 03:48 PM

Thanks Hans, you're not kidding. I'm looking forward to going back to being a hermit again after tomorrow, playing with equations instead of with people.

I think we worked out the pdf problem. Thanks for the tip though Carl.

jal

Nov12-07, 04:49 PM

E8 lives in 8D. Sure, it can be projected down to 3D.
Well ... it's better than dealing with 11D.
Believe me .... I'm trying with what I got ....???
From your statement I get a visual of a proton iceberg.
I looked at your slides .... it should give an interesting presentation.

marcus

Nov12-07, 05:49 PM

...I'm looking forward to going back to being a hermit again after tomorrow, ...

It's been wonderful being able to watch the baby debut. thanks for being here at PF during.
Really smart of Jorge Pullin to invite you immediately to do ILQGS. It is already starting to be runup to next July QG2.

On your sllde #45 in the concluding "discussion of E8 theory" section you say

Quantization:
* Coupling constants run.
* Large Lambda compatible with UV fixed point.
* Just a connection — amenable to LQG, spin foams, etc.

In Reuter's papers Lambda indeed gets large as k -> infty, so he has Lambda run in the right direction for E8 theory's needs.

But the other constant he has running is GNewton which he has go to zero (!) as k -> infty. It seems like an unexpected thing that might cause a stumble, so I mention in case you get into discussing that bullet of slide 45.

Have fun with the ILQGS talk! it will be good for both theories and I hope they can converge some.

strangerep

Nov12-07, 05:58 PM

Desitter space has no Smatrix, [...]
Read there is no apparent Smatrix in the theory!

Hi Haelfix,

I have some followup questions (for yourself, or anyone else who
knows the answers)...

Where can I read more about how DeSitter space has no S-Matrix?
I'm interested in the precise assumptions that lead to that conclusion.
Is the answer trivial in that, if one looks backwards in an expanding space,
there's no such thing as infinitely-separated effectively-free particles
for t \to -\infty? Or is there more to it than that?

If the former, I'm wondering how Garrett could get any cross-sections
out of such a theory which could be meaningfully compared with particle
physics experiments.

For that matter, what are the Casimirs and unitary irreps for the DeSitter
group? I tried some googling, but couldn't find a good exposition of this.

marcus

Nov12-07, 06:35 PM

...Where can I read more about how DeSitter space has no S-Matrix?
...
Is the answer trivial in that, if one looks backwards in an expanding space,
there's no such thing as infinitely-separated ...
It'll be interesting to see what Haelfix says. Thanks for asking. About your guess of a trivial explanation, note that deSitter space contracts and then expands, so if you look back in time you can have infinitely separated paths.

but even without that, after two particles are a lightyear apart who cares? S-matrix could still be a good effective approximation, even if local reality is deSitter shaped. Just my two cents. We'll see what Haelfix says.

Haelfix

Nov12-07, 07:16 PM

Bryce De Witt afaik did a lot of early work on DeSitter space, but I don't really feel like tracking down the references.

Instead theres a readable bit by Witten on it
http://arxiv.org/PS_cache/hep-th/pdf/0106/0106109v1.pdf

Its a little short on details, but he's at least attempting to recover some notion of observables. Yes the main problem is there is there is no good notion of spatial asymptotia nor is their a conformal null boundary. The former could give you correlation functions on the boundary (alla AdS), the latter an SMatrix (Minkowski)

To quote

"The problem with de Sitter space can actually be divided into two parts. One aspect
is that because of the horizon experienced by an observer, one cannot hope to witness
the final state of the whole universe. The other side of the problem, which seems more
acute to me, is that, as indicated above, one also cannot in de Sitter space make sense
in a precise way of what we usually regard as local particle physics quantities. (...) However, an observer in such a universe would have to perform all
experiments with a finite supply of elementary particles and free energy stored up before
the acceleration progresses too far. Under these conditions, it seems doubtful that one
could perform asymptotically precise measurements."

DeSitter space is nasty indeed... Its the biggest theoretical problem imo of this century.

marcus

Nov12-07, 08:20 PM

Hi Haelfix, I was wondering if you would quote that 2001 paper of Witten. Here is a long quote from the page before where you quoted, which explains WHY he is worried about civilization in the future being able to measure stuff with very high precision in an expanding universe, particularly one with positive cosmological constant.

==quote Witten==
In an eternal universe, in the absence of gravity, with a constant free energy supply generated by stars, this makes perfect sense. In a more realistic description of nature, taking the expansion of the universe into account, there are many pitfalls.

De Sitter space (or a cosmology asymptotic to it in the far future) is a particularly unfavorable case for achieving the usually assumed degree of precision. For example, if it is true that the dimension of the quantum Hilbert space is finite, this puts a limit on the conceivable complexity of any experimental apparatus or computational machinery. The
inflation that will occur in the future in de Sitter space puts a limit on the time in which the experiment must be conducted (or the computation performed) before the free energy supply runs down.

Even the concept of an observer in de Sitter space as a living creature making an observation has only limited validity. For life itself is only an approximation, valid in the limit of a complex organism or civilization. There might be a cosmology in which the approximation we call life is better and better in the future, but this requires a process of
adaptation to longer and longer time scales and lower and lower temperatures [15], neither of which is possible in de Sitter space (where inflation sets a maximum time scale, and the de Sitter temperature is a minimum temperature). The approximation we know as life thus breaks down in the far future in an asymptotically de Sitter world, and this will put an end to any measurement (or computation) performed by an observer or civilization in such a spacetime, and hence an upper bound to its precision.

==endquote==

As one can see, his argument is somewhat speculative. It does not present, as far as I can see, any problem with deSitter space or a universe with positive Lambda. Rather it points out problems inherent in human theories which depend on giving meaning to precise asymptotic measurement----measurement at infinity. They don't apply to the world we live in.

The sensible response would seem to be NOT to avoid a particular shape, if it fits our universe, but to go with the observed shape and FIX THE THEORY. I see that as the lesson to be drawn from Witten's paper. So I don't see Witten's paper as particularly relevant to present discussion of E8 theory. Do you agree?

the paper is http://arxiv.org/hep-th/0106109
an expanded version of the talk Witten gave to Strings 2001 at Mumbai, India.

for an updated view of what the future of scientific measurement looks like in the universe we got, see
http://arxiv.org/abs/0704.0221
The Return of a Static Universe and the End of Cosmology
Lawrence M. Krauss, Robert J. Scherrer
Gen. Rel. Grav. 39 (2007) 1545-1550

it seems considerably more dismal than the view Witten evokes
We demonstrate that as we extrapolate the current LambdaCDM universe forward in time, all evidence of the Hubble expansion will disappear, so that observers in our "island universe" will be fundamentally incapable of determining the true nature of the universe, including the existence of the highly dominant vacuum energy, the existence of the CMB, and the primordial origin of light elements. With these pillars of the modern Big Bang gone, this epoch will mark the end of cosmology and the return of a static universe. In this sense, the coordinate system appropriate for future observers will perhaps fittingly resemble the static coordinate system in which the de Sitter universe was first presented.

marcus

Nov12-07, 09:05 PM

DeSitter space is nasty indeed... Its the biggest theoretical problem imo of this century.

I don't understand what you are saying. Witten's vision of scientific measurement in distant future applies to the standard LambdaCDM cosmology which describes the world we live in, in the same way it applies to the simplified deSitter model of it.

How can you call the real world nasty (as it must be by the same reasoning)? Maybe you are joking.

Haelfix

Nov12-07, 09:16 PM

Strangerep asked me about the Smatrix in DeSitter space, so I gave him a paper that tries to explore that.

The relevance is there are no quantum observables (neither local, asymptotic or global) in quantum gravity in DeSitter space. People, like Witten (and others) look for some, but they are hard to construct. Some people use relational variables instead and so forth. Even the nature of the Hilbert space is under dispute (eg is it finite dimensional or infinite), nor do we know what the unitary reps are.

There is nothing speculative about this, thats the state of the art, and hasn't progressed that much for over 30 years b/c of the technical problems with dealing with the space.

The relevance to the E8 paper (which is essentially a classical paper) is in the quantum regime you want to seemlessly connect local DS to local Poincare for lambda --> 0 in the standard model limit. Which is hard to do! Not only b/c of the absence of an SMatrix in the gravity regime, but b/c it already seems like there is a discontinuity in the very action.

marcus

Nov12-07, 10:46 PM

Also, I'll be presenting a talk tomorrow, bright and early:

http://relativity.phys.lsu.edu/ilqgs/

The pdf for the talk just went up five minutes ago, but there seems to be some problem displaying them on windows machines. If anyone has any suggestions on how to fix that, it would be appreciated. (I have a mac)

This new PDF is a big help. CarlB's comment was that "It makes a good addition to the arXiv article."

Here is the direct link to the PDF.
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

======EDIT TO REPLY TO NEXT=====
Thanks Carl, interested by the possible preon angle. I wrote you a PM in reply.

CarlB

Nov12-07, 11:22 PM

Marcus, I'm beginning to suspect that there is a fairly simple preon model hiding behind the E8 here. The paper on octonions by Baez:
http://math.ucr.edu/home/baez/octonions/oct.pdf

shows that E8 is related to the isometries of OxO where O is the octonions. The octonions are not associative, but they are close. If you could adjust the signs in the multiplication table, they would be associative. They are called "alternative" instead of the more general non associative.

When you translate spinors into density operators, you take two of them at a time. This gets rid of arbitrary signs in the spinors, they cancel. This means that when you translate octonionic symmetry operations on spinors into octonionic symmetry operations on density matrices, you end up with a density operator theory that IS associative.

Associativity is important in density matrix theory because it translates into the fact that when you compute a path integral, it doesn't matter whether you start your analysis at the initial and final end.

Another way of saying the same thing is that when you compute the probabilities associated with a system that transitions through the sequence of states A, B, and C, it doesn't matter if you do the computation as (AB)C or A(BC), you should get the same result. And the octonions are compatible with this, when you apply them to density operators (as are required for virtual particles anyway).

So the OxO translates into E8 being a model of composite particles made from two quantum objects with |O| symmetry, where "|O|" symmetry is a density matrix type symmetry you get from (more or less) ignoring signs in the octonions.

Thomas Larsson

Nov13-07, 06:36 AM

The relevance is there are no quantum observables (neither local, asymptotic or global) in quantum gravity in DeSitter space.

Unless, of course, we are missing something essential.

It should be an uncontroversial fact that diffeomorphism symmetry on the circle *is* compatible with locality, in the sense of correlators depending on separation, but only in the presence of an anomaly; unitary Virasoro reps with h > 0 exist, but only if c > 0. This observation was the main reason why I generalized the Virasoro algebra to higher dimensions.

With local observables, it does not really matter if de Sitter admits global observables or not.

Hans de Vries

Nov13-07, 11:42 AM

Where can I read more about how DeSitter space has no S-Matrix?

Is the answer trivial in that, if one looks backwards in an expanding space,
there's no such thing as infinitely-separated effectively-free particles
for t \to -\infty? Or is there more to it than that?

It seems to be just that....

http://online.kitp.ucsb.edu/online/strings98/witten/

The thing what really does seem to hurt is this:

http://online.kitp.ucsb.edu/online/strings98/witten/oh/12.html

\Lambda = 0\ \Rightarrow\ \mbox{S-matrix}

\Lambda < 0\ \Rightarrow\ \mbox{AdS/CFT}

(\Lambda > 0\ \Rightarrow\ \mbox{no AdS/CFT.......})

He's getting more cautious now here:
http://online.kitp.ucsb.edu/online/strings98/witten/oh/25.html

Regards, Hans

ccdantas

Nov13-07, 11:48 AM

Audio for today's talk by Garrett Lisi is posted at
http://relativity.phys.lsu.edu/ilqgs

marcus

Nov13-07, 12:03 PM

Audio for today's talk by Garrett Lisi is posted at
http://relativity.phys.lsu.edu/ilqgs

I've been listening! It's impressive and nicely done. I hear Jorge Pullin but not much interruption by questions so far.

the phrase "suggestively colored dark" commenting on slide #38 is suggestive

this was in reference to the "xPhi" and the "w" symbols at the bottom of the E8 Periodic Table on slide #38.

we have company coming and my wife insisted that I stop listening and help her bake an almond cake
so I only got to hear the first 38 of the 48 slides discussed.

ccdantas

Nov13-07, 12:39 PM

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

Nov13-07, 12:53 PM

I think there was some joke right at the end?

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

marcus

Nov13-07, 01:24 PM

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 :wink: :wink:") 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

Nov13-07, 02:27 PM

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

Nov13-07, 05:24 PM

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

Nov13-07, 07:11 PM

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 :wink: :wink:") 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

Nov13-07, 07:37 PM

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

:cool: gotta love it, right? :biggrin:

garrett

Nov13-07, 08:45 PM

Exactly so.

hch

Nov14-07, 03:44 AM

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 antropic 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

Nov14-07, 09:18 AM

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

Nov14-07, 09:25 AM

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

Nov14-07, 10:15 AM

...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

Nov14-07, 10:20 AM

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

Nov14-07, 11:45 AM

marcus

Nov14-07, 12:13 PM

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

Nov15-07, 11:24 AM

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 doesnt 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

Nov15-07, 11:34 AM

I've started Wikipedia pages for Garrett (http://en.wikipedia.org/wiki/Garrett_Lisi) and the ESToE (http://en.wikipedia.org/wiki/An_Exceptionally_Simple_Theory_of_Everything) if anyone wants to add to them.

arivero

Nov15-07, 01:45 PM

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

Nov15-07, 02:46 PM

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 highschool). But of course, that doesn't mean I'm not interested.

staf9

Nov15-07, 03:02 PM

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

Nov15-07, 03:23 PM

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 occured was with the quarks, which started out as an application of SU(3).

jal

Nov15-07, 06:19 PM

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

Nov15-07, 07:54 PM

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

Nov15-07, 08:13 PM

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

Nov15-07, 09:06 PM

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

Nov15-07, 11:30 PM

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_Everyt hing_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

Nov16-07, 01:07 AM

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

Nov16-07, 02:04 AM

This is all very exciting!

Congratulations Garrett, and good luck!!!

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

marcus

Nov16-07, 03:50 AM

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

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

Nov16-07, 03:51 AM

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 (http://meneame.net/story/cientificos-maravillados-nueva-teoria-todo) 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

Nov16-07, 04:06 AM

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

Nov16-07, 04:33 AM

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

Nov16-07, 10:54 AM

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

Nov16-07, 11:03 AM

Congratulations Garrett!

Thanks very much for staying involved in this thread and the backreaction one :smile: 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

Nov16-07, 02:28 PM

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. 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.

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.

marcus

Nov16-07, 02:36 PM

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

I would guess the trouble I am having is special to my system. I tried twice and loading the applet failed both times. So all I get's a blank grey square field with a red X in upperleft corner.

Of course I'm too busy nailing this down as a preon theory to deal with fixing the rough edges in the above.

A short description of the boson / fermion situation, from the point of view of the roots drawn by the above program (and the ones listed in Table 9 of Lisi's arXiv paper).

The fermions carry quantum numbers of +-1/2, but there are an even number of +s (and therefore an even number of -s too). The bosons are then defined by the minimal changes between fermions.

That is, define a distance function on the fermions given by the sum of squares of the differences between the roots. The fermions 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 bosons are all the ways of choosing two quantum numbers out of 8, with those two quantum numbers being +1 or -1 independently.

This has preon model written all over it.

Thanks for the help on this. I am looking forward to the Java illustration when I get it working.

arivero

Nov16-07, 02:40 PM

CarlB

Nov16-07, 02:54 PM

I would guess the trouble I am having is special to my system. I tried twice and loading the applet failed both times.

Marcus, I've got a lot of other simulations that have been out there for a long time but were developed with an older version of Borland's Java. Could you tell me if my gravitation simulation works here:
http://www.gravitysimulation.com/

Actually, now that I look at his scheme again, I see that my version of bosons and fermions is not what he's doing. I had got into doing the roots and ignored the details of the assignments on page 16 of the paper. I like mine more, too bad it doesn't give the standard model!

marcus

Nov16-07, 03:32 PM

Could you tell me if my gravitation simulation works here:
http://www.gravitysimulation.com/

your orbit applet works fine. It's hard to stop watching it. I was superimposing a spray of Schwarz schild orbits on a spray of Newton.
Everybody's system is different. don't worry about the other which for some reason i can't get.

staf9

Nov16-07, 04:25 PM

http://www.measurementalgebra.com/E8.html

Works great for me, may need to update java to get it working right, very nice job Carl

strangerep

Nov16-07, 04:30 PM

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.

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?

Pages 12-21 of Weinberg vol-III deal with standard C-M. Then on pp21-22 he discusses
the conformal group extension Tony Smith mentioned. To be more thorough, it should be
clarified that Weinberg gives this extension "in theories with only massless particles".

But it seems to me there are other reasons to back off on Coleman-Mandula vs E8
at this time... Some of the other inputs to the C-M theorem are that the "symmetry
generators take 1-particle states into 1-particle states" and "...act on multiparticle
states as the direct sum of their action on 1-particle states". The "1-particle" states
here are the usual momentum/spin unirreps of Poincare.

Now, one doesn't need to read very far into the C-M proof to see that if these
preconditions involving "1-particle states" don't apply, then the C-M proof stops
dead in its tracks very early. In particular, it does not apply to (say) transformations
between inequivalent Fock representations.

But the key reason to back off is that E8 theory is not yet a quantum theory (right, Garrett?).
Hence there is no notion of states of definite particle number, nor even a complete
understanding of how the unirreps are characterized. So let's wait until if/when it
gets developed into a proper quantum theory.

jal

Nov16-07, 04:30 PM

CarlB
It's fine for me.
However, you would need to include the effects of spin.
ie. Use a 2d surface.
edge,front,edge,back,edge,front (cannot see edges)

Coin

Nov16-07, 05:00 PM

strangerep, thanks for the clarification.

Nereid

Nov16-07, 08:21 PM

From Bee's blog: At 2:03 PM, November 16, 2007, Lumo said...

Dear "Almida",

I assure you that Perelman's precious results have been peer-reviewed several times, for example in Journal of Asian Mathematics (http://www.arxiv.org/abs/math.DG/0612069).Did Lumo, here, with some subtlety, threaten to 'do a Yau (http://www.amazon.co.uk/Poincares-Prize-Hundred-year-Greatest-Puzzles/dp/0525950249/ref=sr_1_1/202-4092582-0484661?ie=UTF8&s=books&qid=1195265966&sr=1-1)' on Garrett?

CarlB

Nov17-07, 02:50 AM

Given that I wrote the E8 applet last night, I should be sleeping now, but instead I fixed a few bugs and added a group theory color drawing feature.
http://www.measurementalgebra.com/E8.html

I added the ability to change colors according to the F4 and G2 representations. To do this, click the "Colors" button. This will bring up another window where you can change colors of things. To change F4's "8V" component, click the F4 button until it shows "F4 8V". Leave the G2 button as "G2 All". Choose a color, and click OK.

If you want to select colors at the F4 x G2 level, click the F4 and G2 buttons until they show the two components you want to look at, select a color, and click OK. The roots that are in that intersection will change color (if there are any). You can change the color of the background by selecting a color, and clicking "Bkg". When you're done, click "Exit".

This all gets back to Table 9, page 16 of the Lisi paper. There is a bit of a confusion in the bottom 3 lines of the table. These last three lines are labeled as q_{II}, q_{III} for the G2 component, but actually the roots described include also \bar{q}_{II}, \bar{q}_{III}. I'm sure these were abbreviated to keep the table's size under control, but it briefly confused me.

Next, I'll probably add the ability to change the shapes drawn. That should give you most of the capability of making your own

Hans de Vries

Nov17-07, 12:15 PM

shoehorn

Nov17-07, 12:49 PM

An acid comment at Motl's blog asks to recover the units, ie to put all the hbar and c and G in its place. Actually, it could be a good idea in order to see what is preserved in the classical limit, what is lost, what can become a classic field, and what goes to null as field and appears only as particle. As I said before, a lot of the work of a TOE should be to worry about the limits to recover the previous theories.

EDITED: Motl boasts of a triplication of the traffic of its blog. Looking to my own stats, my guess is that all the physics blogosphere have got this *3 factor. (Incidentally, Motl implies about 2500-3500 regular visits to his blog.)

Lubos' "claims" are, unsurprisingly, disingenuous junk. He's used google trends to search for the terms "motl", "woit", and "smolin". He fails to point out that the results returned by Google trends are of no relevance to the traffic to any blog; they are simple indicators of the frequency with which each term was searched. As an example, people looking for Lubos' blog by doing a google on "motl" contribute just as much to the google trends results as do those who are looking for other people called "Motl".

It's terribly sad to see what Lubos has become. He showed such promise at one stage.

Molon Labe

Nov17-07, 08:16 PM

datakleptomanic

Nov18-07, 01:25 AM

i am agog! last time i checked on my IQ it was up there somewhere... but holy moly! batman

check

Nov18-07, 04:46 AM

Just wanted to jump in and say congrats to garrett! I admit the details of this paper are beyond my comprehension but I understand the basics and its potential.

arivero

Nov18-07, 06:17 AM

In this paper http://arxiv.org/PS_cache/hep-ph/pdf/0207/0207124v1.pdf Witten states:

"Of the five exceptional Lie groups, four (G2, F4, E7, and E8) only have real or pseu-
doreal representations. A four-dimensional GUT model based on such a group will not
give the observed chiral structure of weak interactions."

Can someone, in a general sense, explain how Lisi purports to work around this? That is, how does Lisi produce the "observed chiral structure of weak interactions"?

This is absolutely not a challenge to Lisi. I have little understanding of this and I am simply trying to make connections.

Thanks for suggesting this reading! I'd add that people interested on GUT should also look for a collection of reprints done by Zee time ago and published with a black soft cover in two volumes (but GUT is mainly the first one).

The chain in formula 7 of Witten paper is the traditional argument up to E8. Also some SO(2n) chains, not only in extra dimensions -as Witten says in the next page- but also in four dimensions. It was not clear if the need extra dimensions were, after all, a question of interpretation. What happens with SO(12) and SO(16) is that they are able to reproduce V-A, but they also have V+A interactions and you must break them. But yes, it seems that the restoration of hopes for E8xE8 come exclusively for extra dimensional theories, because Witten found a way to break the symmetry not into E8 but into a subgroup of E8 getting at the same time only V-A unbroken, and this was using very peculiar choosings in the compactification of the extra dimensions. Not peculiar enough, regretly, and then string theory went to its current stalemate situation. This resumes the rest of the paper.

------------------------------

Now, the point is about a subgroup inside E8xE8, and at the current level of development, even the E8 of Lisi could have some role; do not forget stringers have been very good about taking developments from other fields. A non trivial inclusion E8 \subset E8 \otimes E8 (not the obvious trivial one) could in turn be a clue to the right choosing of the V-A compliant subgroup.

Why do I still expect something in E8xE8? Because if you look ot representation level, this is build as pair of particles. And then the known peculiarity of quark pairs in the standard model is that all of these pairs, for the five lightest quarks, reproduce again, with the exact counting of degrees of freedom, the particle content of the standard model (only that if taking literally, all these pairs are bosons). This is a very particular (can not tell if "exceptional") point that only happens with three generations and five light quarks.

DataPacRat

Nov18-07, 10:04 AM

I'm yet another interested reader who understands most science magazines and reporting, but doesn't have a clear understanding of what a 'manifold' is.

I understand that Lisi is proposing that the 240 roots of the E8 group correspond to the various particles and forces, and that each root has 8 coordinates. However, as an amateur, I have trouble deciphering which particle is represented by which combination of letters, superscripts, subscripts, arrows or lines over the top, and so forth, let alone the coloured triangles in Lisi's diagrams (however pretty they are). Would it be possible for somebody to write out a basic text file with, say, 240 lines, each of which has the 8 coordinates, and an English description of Lisi's assigned particle such as "photon" or "bottom anti-quark"? (If there is a specific significance to what any of the coordinate numbers mean, an introductory mention of which one is 'spin' etc would also be nice.)

Thank you for your time.

ericchou

Nov18-07, 12:33 PM

Congratulations to Garrett!!!

I don't know about physics. And I can't read english much.

I know your news from Taiwan media. I think you do a great thing.

In my office, I download your paper, and print it. My workmate laugh me " you don't know english, and you don't know physics. why you download it?" Although I don't know physics, But I see figure 2,3,4 in your paper, rotate & rotate. I know some thing happened. a beautiful structure.

So I think you are right.

Thank you.

eric

staf9

Nov18-07, 09:02 PM

In recent news on people "jumping the gun," I've heard of people doing some serious work on E8 Theory even though the paper was posted a whole 11 days ago and we can't really confirm it until the LHC confirms/disproves the existence of the missing particles in E8.

Personally I think there's a good chance of E8 being right, so I'm kind of jumping the gun by saying that but certainly not as much as people who are already starting to research other relationships in particle physics using E8 as a basis.

I'm sure this has been done over and over again when people see some light in a theory though, so nothing new. And who knows, someone may discover something that could prove E8 right or wrong.

marcus

Nov18-07, 09:48 PM

...I've heard of people doing some serious work on E8 Theory even though the paper was posted a whole 11 days ago ...

that's exciting. do you happen to know where? connected with what institution?
(never mind that's just how my mind works:smile: )
it's an awful lot to ask that a dark horse independent approach be taken on at a good research institution but I sure hope that happens

staf9

Nov18-07, 10:27 PM

that's exciting. do you happen to know where? connected with what institution?
(never mind that's just how my mind works:smile: )
it's an awful lot to ask that a dark horse independent approach be taken on at a good research institution but I sure hope that happens

It's more of individuals (string theorists) who are trying to disprove E8 Theory. This was mostly a word-of-mouth thing that I heard and I don't mean to be spreading any rumors, but it isn't too tough to believe since E8 does rule out string theory.

It would be really great if a research institution did take a closer look at the theory though. That would get my hopes up.

When I read Garrett's paper, there were a bunch of unexplained phenomena that ran through my mind when he mentioned missing particles in E8. Plus, it got me thinking about the different possibilities of unification of gravity and the standard model if using E8 is wrong. Hopefully, it did that same thing for someone much smarter than I am.

My ever changing opinion on this topic is at the point where, realistically, I think the theory has a small chance of being right.

But, the light at the end of the tunnel is that E8 theory and the work that results from E8 may clarify certain aspects of particle physics and the unification of gravity and the standard model so that someone in the future may be able to answer these questions.

In other words, I don't believe E8 theory has to be 100% correct in order to answer a few of our questions about the universe.

Hdeasy

Nov19-07, 12:18 PM

Yes, congrats to Garrett. It is really a wonderful achievement. Elsewhere I made the point that there are certain similarities with Heim Theory. E.g. even though HT doesn’t have explicitly E8 in it, it’s dimension law throws up 57-dim. The symmetries of E8 represent a 57-dimensional solid .

I found out, by playing with Heim's dimension law for n dim embedded in higher dimensional space of N dim::

N = 1 + Sqrt(1+ n.(n-1).(n-2))

Heim's solutions to this were
n = 4, N = 6 (basic HT for mass formula etc.)
n = 6, N = 12 (EHT with 8 dimensions as the main ones, but 4 additional time like ones that are involved in determining the QM probabilities - and I think something of this sort was mentioned for Lisi's theory too... or am I imagining it?)

The next solution after the ones listed by Heim was:

n = 57, N = 420

And indeed there are no others for n < 1000.

Interesting to see gravi-electroweak effects in Lisi’s theory – reminiscent of the gravito-photons of HT, which successfully predicted the Tajmar artificial gravity effect to within an order of magnitude, beating GR by more than 20 orders in that sense. One or 2 groups are lending tentative confirmation to the Tajmar effect – more definite reproduction efforts should report in soon. If they are positive, then it looks good for HT’s 2 extra G-forces, and so a SO (10) unification might be on the cards. It would then be a question of how that tied in with E8.

arivero

Nov19-07, 02:42 PM

How is it that nobody is intrigued about the fermion doubling in table 9 of the paper? Is it some obscure interplay between complex and real representations?

arivero

Nov19-07, 03:48 PM

The old E8
http://www.slac.stanford.edu/spires/find/hep/www?j=PRLTA,45,859

Grand Unification with the Exceptional Group E8

I. Bars and M. Günaydin *
Physics Department, J. W. Gibbs Laboratory, Yale University, New Haven, Connecticut 06520

Received 14 April 1980

A truly unified model of the basic gauge interactions, except for gravity, based on the exceptional group E8 is proposed. The fundamental fields belong to the smallest possible single representations for each spin. In addition to accounting for the three "observed" SU(5) families, this Letter predicts the existence of three more conjugate SU(5) families below 1 TeV.

and its bandwagon (well, the whole train if you click "Next")

http://www.slac.stanford.edu/spires/find/hep?c=PRLTA,45,859

Note also
http://arxiv.org/abs/hep-ph/0401212
http://arxiv.org/abs/hep-ph/0201009
Should $E_8$ SUSY Yang-Mills be Reconsidered as a Family Unification Model?
Authors: Stephen L. Adler

starkind

Nov19-07, 03:56 PM

Fredrik

Nov19-07, 05:10 PM

It's more of individuals (string theorists) who are trying to disprove E8 Theory. This was mostly a word-of-mouth thing that I heard and I don't mean to be spreading any rumors, but it isn't too tough to believe since E8 does rule out string theory.
Does it? If you don't mind, can you explain how? Preferably in a way that someone like me can understand? (I know the basics of QFT and GR, but not the fiber bundle stuff. I know what a bundle is, but not much more beyond that (for the moment)).

arivero

Nov19-07, 05:19 PM

arivero

Could you say more about this? I looked at the table and noted that the fermions in lines 4 through 15 are double, but it seems that the doubles here are matter-antimatter pairs, if I am right about the bar notation above the lower set of pairs meaning antimatter. Is that what you meant? I am struggling in deep water here and anything you say might give me a lifeline.....

Thanks

Well, the last column in each row of the table is "#" and it counts the number of components, from the 248, that are accounted for in the row. For 4 fermions in a row, the # counts 8 components for a row of leptons (or a row of antileptons) and, obviously, a factor 3 for a row of quarks (or a row of antiquarks). Now, this does that the leptons for one generation, when you count particles and antiparticles, have a total # of 16, while in reality they have a total 8 degrees of freedom, so they? So it seems that the particles are duplicated; if it is so, well, duplication is an effect already noticed in old 1980 E8 unification and not completely out of the orthodoxy. But I'd expect it to be explained with some detail in this new context. Is it?

Coin

Nov19-07, 07:35 PM

So I've got various questions about this E8 thing, and I'm not sure whether to ask them here or in the "layman" thread (I am in the somewhat awkward position of being very much a layman with regard to the physics here but having a somewhat more technical perspective with regards to the math). I'm interested in E8 because I have had a lot of trouble understanding yang-mills/gauge theories, and it seems like-- even as speculative as it is-- studying E8 might be a good way to learn about the general principles of these things, because E8 is in a certain sense simple compared to the Standard Model (even if it is only simple because there is so much we don't know about it yet :smile:). Before I can do that though I want to be able feel like I understand the mathematical structure that is E8 itself.

From looking at wikipedia (http://en.wikipedia.org/wiki/E8_%28mathematics%29#E8_root_system) and this page (http://aimath.org/E8/e8.html) (I think from the people who "mapped" E8 awhile back?), the impression I get is that E8 consists of those vectors of length 8 that can be formed from adding together integral multiples of the members of a basis of "root" vectors. The group operation appears to be vector addition, and the "root" vectors consist of all 8-vectors of the form
<±1, ±1, 0, 0, 0, 0, 0, 0>
or
<±0.5, ±0.5, ±0.5, ±0.5, ±0.5, ±0.5, ±0.5, ±0.5>
Because there are 8-vectors which it is not possible to construct by adding together these roots, E8 forms a proper subset of the set of {all vectors of length 8 consisting of integer or half-integer values}.

Is all this correct? Okay, so: If so, is this the E8 Lie group or the Lie algebra? In either case, what is the corresponding algebra/group? And in the case of the algebra, what is the lie bracket? (The atlas page says only that the lie bracket for E8 is "very hard to write down". Oh.) And finally, is it "weird" that E8 is a lie group/algebra-- yet has only a countably infinite number of members, and is apparently constructed entirely of discrete structures? I've thus far only encountered lie groups which are continuous, where it makes sense to talk about things like "infinitesimal generators". There doesn't seem to be anything infinitesimal about E8 at all. (Mind you, I'm not complaining-- I have a CS background and I am WAY more comfortable with anything discrete than I am with anything continuous! It just seems jarringly different from the way I understood people to use lie groups/algebras previously, and I'm confused how I missed this.)

Past this, the biggest thing that is confusing me here are the "roots". First off, although this is probably not all that important, how on earth were they chosen? That is to say, was someone just playing around with addition on different sets of basis vectors, and went "oh hey this particular combination of 248 vectors acts kinda weird, everyone else come look at this"? Or was E8 first discovered as some other kind of structure, and it was later realized that the 8-vectors above are a convenient representation of that structure? Second off and more importantly, I am dreadfully confused by these root "diagrams" such as one finds all over Lisi's paper. As far as I can tell, the idea is that we plot each of the roots as a point in eight-dimensional space. (I take it that we plot them by simply treating each 8-vector as a coordinate?) However, then we for some reason draw lines between some of the roots! Why on earth do we do this? What do the lines mean?

I'm similarly a little bit confused by this "simple root" thing that wikipedia describes. As far as I can tell, the "simple root"s are an alternate integral basis for E8, consisting of the eight vectors found in the rows of this matrix:

http://upload.wikimedia.org/math/7/5/b/75bce2aa3f595732bd54baa61e503070.png

Wow, that's convenient! What's confusing me here though is, why on earth do we bother using the 248 roots described above, when we could just use these 8 simple roots and be done with it? Another thing confusing me: Wikipedia offers a "dynkin diagram" (which I take it is different from the "root diagrams" used with the 248-root system) which looks very deep and beautiful:

http://upload.wikimedia.org/wikipedia/en/d/d3/Dynkin_diagram_E8.png

... but I can't for the life of me figure out what it's supposed to mean. Wikipedia says that this is a graph where vertices represent members of the simple root system, and edges are drawn between any two members of the simple root system (I assume this means a 120 degree angle when we treat the simple roots as coordinates in 8-space.) Okay, that's nice, but why? Why do we care which members of the simple root system are at 120 degree angles to one another?

I have a couple more questions related to what Garrett in specific is doing, but these are just my questions about the E8 [group? algebra?] itself. Any help in figuring these things out would be appreciated. In the meanwhile, something vaguely frustrating me is that there does not seem to be any specific information on E8 in the obvious places. It is clearly a well-researched subject but the best I can find is these very vague wikipedia-style summaries, and John Baez's writeups (which are invariably exhaustive and lucid, but everything I've found which Baez has written covering E8 seems to be primarily about other things, like octonions, and only indirectly concerned with E8). Is there some particular thing, perhaps a book, I would be best served by going and reading if I am curious about the mathematics of E8?

staf9

Nov19-07, 08:47 PM

Does it? If you don't mind, can you explain how? Preferably in a way that someone like me can understand? (I know the basics of QFT and GR, but not the fiber bundle stuff. I know what a bundle is, but not much more beyond that (for the moment)).

At a first glance, it's easy to think that E8 and string theory can coexist on some level.

There were a few things that made them mutually exclusive in my eyes after a while though, some of which were pointed out on forums that Garrett posted on.

String theory (specifically supersymmetry) uses a super Lie algebra to package bosons and fermions together. E8 uses simple (and possibly graded in the future, depending on where the theory goes) lie algebras to replace anti-commuting 1-forms with Grassmans.

String theory was vague to me when it came to determining how many dimensions to use to describe the universe, though I believe 10 spacetime dimensions (or 11 spacetime dimensions for M-Theory) is what is used. E8 Theory uses a 4 dimensional base manifold with 8 mathematical dimensions since the e8 root system can be rotated in that many dimensions. E8 theory is a "do or die" theory, it states its parameters meaning it can be verified or proven wrong about these things unlike many of the other theories today.

I may have missed many other things; just the basis of the two theories seem very different and at some points contradictory to me.

staf9

Nov19-07, 09:25 PM

To Coin - here's some helpful websites for E8:

http://aimath.org/E8/e8.html

http://math.mit.edu/~dav/E8TALK.pdf (the narrative, http://atlas.math.umd.edu/kle8.narrative.html, is a pain to read)

E8 is an exceptional Lie group, specifically a Lie group for an icosahedron, or 20-faced polyhedron, maybe looking up search terms with regards to that might help. When I read Garrett's paper I had to look up Lie algebra and groups on wikipedia to remember a bunch of the math.

jal

Nov19-07, 10:14 PM

Coin!
you said, "... the impression I get is that E8 consists of those vectors of length 8 that can be formed from adding together integral multiples of the members of a basis of "root" vectors.... "

wiki says, "Each of the root vectors in E8 have equal length. It is convenient for many purposes to normalize them to have length √2."

and http://aimath.org/E8/e8.html says something interesting, "...This lattice, sometimes called the "8-dimensional diamond lattice", has a number of remarkable properties. It gives most efficient sphere-packing in 8 dimensions, and is also the unique even, unimodular lattice in 8 dimensions."
------
The layman thread is not up to this speed ...yet.
--------
staf9
Your links used a different approach to explain. It wasn't good for me. I probably will help the "pros."
jal

Coin

Nov20-07, 01:55 AM

Jal, I'm sorry, I slipped into CS-ism there. When I said "vector of length 8" I meant something more like "vector of dimension 8". I was trying to express that there were 8 items in the vector. (Actually I guess technically "dimension" is the wrong word there too-- although E8 itself is eight dimensional...)

(And the length √2 thing applies not to E8 in general, but only to the root system people like to use... hmm, come to think of it, is that why we use the 248-element root system rather than the 8-element "simple" root system as the basis? I mean, is the appeal that the elements of the 248-element root system are all the same vector length, √2, whereas the elements of the simple root system are of different lengths?)

Fredrik

Nov20-07, 09:09 AM

At a first glance, it's easy to think that E8 and string theory can coexist on some level.

There were a few things that made them mutually exclusive in my eyes after a while though, some of which were pointed out on forums that Garrett posted on.

String theory (specifically supersymmetry) uses a super Lie algebra to package bosons and fermions together. E8 uses simple (and possibly graded in the future, depending on where the theory goes) lie algebras to replace anti-commuting 1-forms with Grassmans.

Let's see if I understand what you're saying... String theory implies supersymmetry. Garrett's E8 theory doesn't contain supersymmetry at all. Therefore, the two are incompatible. Is that the gist of it?

String theory was vague to me when it came to determining how many dimensions to use to describe the universe, though I believe 10 spacetime dimensions (or 11 spacetime dimensions for M-Theory) is what is used. E8 Theory uses a 4 dimensional base manifold with 8 mathematical dimensions since the e8 root system can be rotated in that many dimensions.

I don't understand that last sentence. Does E8 theory say that space-time is four-dimensional?

jal

Nov20-07, 10:24 AM

A quote from Garrett
http://fqxi.org/community/forum.php?action=topic&id=107
TOPIC: An Exceptionally Simple FAQ
For a magazine image, you may want to use the image of G2 and use some arrows and text box overlays to describe how the interactions between particles correspond to visually adding together the points in these diagrams. This will be the best part of this theory for most people -- you can actually determine how all the particles interact by how these points add together in these pretty pictures.

For example, if you look at the picture of the G2 root system in the paper: Take the green up triangle (that's a green quark) and add the blue circle on the far right (a red-anti-green gluon) and you get the red up triangle (a red quark). This is how the quarks interact with the gluons. It's vector addition -- maybe you can overlay some arrows over the G2 picture to describe how this works for your readers.

When we do the same thing with the points in any of the E8 pictures, we get all the interactions between all the particles. :)

The E8 root system, which is what's shown in the pictures, is a pattern of 240 points in 8 dimensions. This pattern of points describes the shape of the E8 Lie group, through its Lie algebra. The pattern in 8 dimensions is projected onto the 2 dimensional page from different angles to make the different pictures. By understanding this pattern, we get a better understanding of the E8 Lie group.
The elementary particles correspond to points in the E8 root system, which correspond to elements of the E8 Lie algebra, and thus to symmetries of the E8 Lie group.
That's correct -- this E8 Theory only works in four dimensions.
-------
coin ... go and do a search/revue for the concept that are contained in the quote. It might help to do some different visualizing.
http://aimath.org/E8/e8.html says something interesting, "...This lattice, sometimes called the "8-dimensional diamond lattice", has a number of remarkable properties. It gives most efficient sphere-packing in 8 dimensions, and is also the unique even, unimodular lattice in 8 dimensions."
jal

staf9

Nov20-07, 12:02 PM

Let's see if I understand what you're saying... String theory implies supersymmetry. Garrett's E8 theory doesn't contain supersymmetry at all. Therefore, the two are incompatible. Is that the gist of it?

Somewhat, it's more of the way they treat bosons and fermions that makes them different.

I don't understand that last sentence. Does E8 theory say that space-time is four-dimensional?

Yes, E8 theory only works in 4 spacetime dimensions, and all types of string theory describe many more dimensions than that. That's really the major contradiction in my eyes.

marcus

Nov20-07, 04:22 PM

Yesterday the French newspaper LE MONDE had a pretty nice article and interview with Garrett. The article had some quotes from Carlo Rovelli and a range of other people.

Here's the interview, in printerfriendly version:
http://www.lemonde.fr/web/imprimer_element/0,40-0@2-3244,50-979854,0.html

Here's a Babelfish translation of the interview:
http://babelfish.altavista.com/babelfish/trurl_pagecontent?lp=fr_en&trurl=http%3a%2f%2fwww.lemonde.fr%2fweb%2fimprimer _element%2f0,40-0%402-3244,50-979854,0.html

==babelfish version of interview==
Anthony Garrett Lisi: "the theory is mathematically and aesthetically superb"
LEMONDE.FR | 19.11.07 | 14h00

Amateur physicist, Anthony Garrett Lisi, posted, at the beginning of November, on a webserver, a paper of 31 pages stipulating that all the laws of the universe would be described by one and the same theory. This 39 year old American, until now unknown, is attached to no university, any laboratory. His work is not less, since the beginning of November, at the center of sharp discussions in the scientific community.

How do you work ? Who finances your work?

I obtained my doctorate 10 years ago and I left the academic world to work with my own ideas on physics and surfer with Maui. I worked just enough to earn my living, dedicating the majority of my time to the equations and benefitting from the full air.

Then, one year ago, I applied for a grant at new private foundation, Foundational Questions in Physics and Cosmology (FQXi). I obtained it.

I have now a sufficient financing to live, make physics and to offer some boards of surfing to me. Without the support of FQXi, I would not have had sufficient time to devote me to physics and to achieve this work.

Since when do work you on this subject?

Since approximately 10 years. But progress was not continuous. I tried to build several other models which did not function and I had on several occasions all to begin again since the beginning.

If nature says to you that your ideas are false, it is useless to discuss. The "E8 theory" is mathematically and aesthetically superb and until now, it seems to correspond with physics that we know. But that is still new and can, of course, to prove to be false.

How are your work perceived by the physicists of the academic world?

By receiving the support of the foundation FXQi, I thought of having to communicate on my work. When I presented my work at conferences, several physicists of the academic world were immediately impressed by the theory as a whole. Even if I were an outsider, the ideas liked.

This favorable impression grew in the scientific community. And when I published paper, there were an astonishing interest and an attention. I was amazed.

There are also skepticism and criticisms, but that is necessary and healthy. Mathematics used is complex and that will take weeks with the best physicists to go fully at the bottom of the things. I know that mathematics is correct but more work and, then the experiment, will determine if this theory agrees with nature.

How many new particles are they predicted by your theory ? Some criticize reproach him not for predicting the mass of it...

In its current state the theory predicts the existence of 20 new particles. Because the theory is not completely developed, that can however change.

With this theory, it is "all or nothing". There are not a possibility of fudge the parameters or whimsical additional structures. Today, the theory has a satisfactory aspect, but there are still things to specify. With other researchers, we will work to improve the theory and the predictions will result from this.

Would you accept a station in a university?

Only if it is beside a beautiful mountain where to make snowboard.

Why not have carried out a traditional academic career?

I wanted to live in a beautiful place, where I could make surfing or snowboard and work on my physics, without other responsibilities.

I am a contemplative hedonist - I want life of the intense pleasures. And all that wants to say not to pass too much from time in a laboratory, but to find a balance between thinking and having fun.

==endquote==

Here's the main article, with the balance of opinion quotes from other physicists:

The main article, and printerfriendly version:
http://www.lemonde.fr/web/article/0,1-0@2-3244,36-979858@51-979860,0.html
http://www.lemonde.fr/web/imprimer_element/0,40-0@2-3244,50-979858,0.html

Fish translation of the article
http://babelfish.altavista.com/babelfish/trurl_pagecontent?lp=fr_en&trurl=http%3a%2f%2fwww.lemonde.fr%2fweb%2fimprimer _element%2f0,40-0%402-3244,50-979858,0.html
http://babelfish.altavista.com/babelfish/tr?doit=done&url=http://www.lemonde.fr/web/article/0,1-0@2-3244,36-979858@51-979860,0.html&lp=fr_en

chrisina

Nov22-07, 05:43 AM

Congratulations Garrett ! Hope you will get suport from as many researchers are needed to make the necessary calculations which will be needed. It is indeed a beautiful mathematical hypothesis, let's hope that it ends up being the real description of nature, at least it's definetly a new avenue that is worthwile following.

One question I have, which I can't seem to get clear from the paper, how many degrres of freedom does the theory have in the end ? I mean, you explain that one should be able to derive the different mass relationships and coupling constants from the Higgs VEV, as well as the Cosmological Constant (which varies over time according to a relation to be derived I guess), so does that mean that all the parameters of the standard model, as well as the Lambda CDM densities could be theoretically derived from the Higgs VEV ?

Can you also be more precise with what you mean with the coupling constants "run".

Thanks.

marcus

Nov22-07, 10:52 AM

Update.
Jacques Distler has gotten around to responding
http://golem.ph.utexas.edu/~distler/blog/archives/001505.html
http://golem.ph.utexas.edu/~distler/blog/archives/001505.html#more

sorry to cover up the preceding post, by chrisina, which has some questions addressed to Garrett.

=======================
BTW chrisina you asked G.L. what is meant by saying coupling constants run.
It is a usual thing in quantum field theories for the constants to vary with proximity or energy for example the usual value of alpha the fine structure constant in QED is 1/137.036...
but this is not correct for very close approaches. the true or "bare" value at extreme proximity or energy is larger.
as we reduce the energy and increase the scale the coupling constant runs down to it's usual value of around 1/137.

In the QG literature one finds widely scattered references to the idea that the gravity constant G could have a "bare" value relevant at very small scale which is different from the value we measure at macro scale. In other words a number of people seem to suspect that the G constant might run as well. Technically, I should be talking about a dimensionless form of G since I don't know what it means for a dimensionful quantity to run.

If you want to see how this idea is used, you could look up the most recent paper by Reuter and Bonanno. They make extremely bold use of the running (dimensionless) coupling constants idea in a gravity context. Use it to understand stuff about the early universe.

this is in case Garrett does not get around to replying immediately---something to think about in the meantime. Hopefully he'll straighten it out any misconceptions if I've made an error.
======EDIT TO REPLY TO NEXT=====

Hello again chrisina, you were asking G.L. about the number of free parameters in his model, in post #142.
I do not know of any free parameters. But I shouldn't interfere. G.L. is the only person who can really answer that.

My own take on it is there are no free parameters and you get "bare" values of stuff. Like he gets a definite value of Lambda the cosmological constant and he can't do anything about it.

You might want to look at the recent paper of Pereira and Aldrovandi. They also have a microscopic highenergy value of Lambda playing a role----and it would presumably run down to the macroscopic observed value that astronomers tell us they measure.

That is, the whole business is strange and new but G.L. isnt the only one for whom Lambda acts this way. And of course there is the whole Reuter Percacci AsymptoticSafety thing.

So in some sense you could say G.L. has no free parameters but you also have to say that he is in the early stages of developing the theory and deriving stuff, and maybe the present model does not govern how the constants run (making it among other things harder to test experimentally). But we'll see.

chrisina

Nov22-07, 12:09 PM

thx Marcus, what about the number of free parameters ?

Coin

Nov22-07, 02:34 PM

E8 is an exceptional Lie group, specifically a Lie group for an icosahedron, or 20-faced polyhedron, maybe looking up search terms with regards to that might help.
Thanks, I'm trying to look some of this stuff up, also the links garrett posted in the "layman" thread look useful. Just to be clear though-- I am seeing this reference in several places that E8 is the lie group of an icosahedron (and for that matter E6 is same for a Tetrahedron and E7 is the same for an octahedron). This seems like a very interesting way to approach E8, however I am not sure what we mean when we say it is the "lie group". Do we mean that it is the rotational symmetry group? An old Jacques Distler post says that the subgroup of SO(3) which is the icosahedron's rotational symmetry group "can be shown to map to" E8, but I am not sure if this means that they are isomorphic or just that there is an injection or what.

Wikipedia has an article on Icosahedral symmetry (http://en.wikipedia.org/wiki/Icosahedral_symmetry) claiming the symmetry group of an icosahedron to be "I_H", and they describe a symmetry group that seems pretty different from E8. However they include reflection and translation in their symmetry group...

Blackforest

Nov22-07, 02:53 PM

First of all I want to apologize for what I shall say now.

I don't want to disturb the actual "euphory" but did some one heard about the conferences of Hawking:
"Is the end in sight for theoretical physics?" Cambridge april 1980

And :
"The edge of space time." (The new physics; Cambridge press, ...)

The only thing I want to note here is that the E8 theory was stil known at this time. Thus it is nothing really new I think.

Why so much noise ?

notknowing

Nov23-07, 01:06 AM

marcus

Nov23-07, 07:35 PM

possibly useful exchange on Jacques Distler's blog between J.D. and G.L.
http://golem.ph.utexas.edu/~distler/blog/archives/001505.html#c013271

CarlB

Nov25-07, 09:29 AM

possibly useful exchange on Jacques Distler's blog between J.D. and G.L.
http://golem.ph.utexas.edu/~distler/blog/archives/001505.html#c013271

I think that Garrett is being very conservative in his rewriting of physics. He's trying to draw outside the lines by squinting a bit and that really doesn't work so well.

Instead of insisting that "New Physics" be completely compatible with all the theory of the "Old Physics", it needs to be compatible only with the experimental results of Old Physics. If the theory of old physics was perfect it wouldn't be so difficult to reconcile general relativity with quantum mechanics.

The essence of what the old physics knows about quantum mechanics is distilled into the Standard Model. If a new physics reproduces the standard model on a simpler set of assumptions than the old physics, you have to give more credit to that new physics than you gave to the old. Sure the old physics assumed restrictions such as Coleman-Mandula etc., but Coleman-Mandula is not an experimental result. It is a theoretical constraint that is built on a rather long and involved chain of reasoning. So long as a New Physics gets the standard model, you cannot use experimental arguments against it, only theoretical ones.

But new physics theories have ALWAYS violated the theoretical restrictions of the old physics. That is why they are new. What new physics must do is to reproduce what is predictive in the old physics, it does not have to match exactly the methods for getting those predictions.

I think that Garrett did violate the theoretical limits of the old physics in packing the standard model plus gravity into E8. But I don't think this matters. If Einstein rolls over in his grave that's okay; hey, that's what new physics always does to old physics. If the people who staked their careers on understanding the exact details of the old physics scream bloody murder, that's even better.

History shows that when new physics arrives, it is never accepted by a majority of the old physicists. Instead, the battle is fought among the new generation. The old physicists eventually die. All you really need to know is that Garrett's theory is appreciated by a few; new physics never wins a majority (until there is an experiment that decisively supports one of its predictions).

PhilosophyofPhysics

Nov25-07, 10:13 AM

"All truth goes through three stages. First it is ridiculed; then it is violently opposed; finally it is accepted as self-evident." -Schopenhauer

10st1denTT

Nov25-07, 04:04 PM

sadly stages one and two do not determine a phase three outcome, right(?)
so your (schopenhauer's) apt observance qualifies better for a a posteriori musing (philosopher style:))... there is not much Predictive Power in it
The hard work has to be done now!
But not by me :)
The media frenzy garanties that the paper will be scrutenized (and sink to shame(?) or fly to glory). What will not happen is that it simply gathers dust in a dark basement shelf (as has fared to many a fine theory before).
So things are on a deterministic road now anyway.

marcus

Nov25-07, 05:06 PM

"All truth goes through three stages. First it is ridiculed; then it is violently opposed; finally it is accepted as self-evident." -Schopenhauer

:biggrin:

...
The media frenzy garanties that the paper will be scrutenized (and sink to shame(?) or fly to glory). What will not happen is that it simply gathers dust in a dark basement shelf (as has fared to many a fine theory before).
So things are on a deterministic road now anyway.

Lost I,
nice summary.

The issue of the huge wave of public admiration and media attention has come up.
1. is the publicity harmful to the longterm interests of science?
2. is it harmful to the development of E8 theory? (say, by making it less likely that other physicists will want to help Garrett Lisi work out the bugs, derive predictions, and complete the picture)
3. is it harmful to G.L. personally, if not to his theory's prospects?

Does anybody have thoughts about this?

My personal opinion is that the admiration and attention do no harm (aside from possibly provoking anger on part of those with competing demands for science media stature and glamor).

I think it's fine for the public to be exposed to attractive images of scientists. I don't see any harm in a short run of media enthusiasm. Things like this die down after a few weeks and leave no permanent expectations to be disappointed. What actually are we afraid of? What is supposed to be the harmful consequence to science?

I think the several decades of hyping string theory as a Theory of Everything, teaching a generation of adolescents to expect it to provide the final answers---a concerted effort involving public statements by many scientists---has been harmful to science. By debasing standards of empiricism and raising unreasonable expectations. But that is on a different scale.
==================

What I do think has been harmful is what I see as vindictive and relentless hammering of an incipient theory on a handful of science blogs.
I don't completely understand the motivation for all the anger I heard. Some of it came from string theorists, of course, and could have been motivated by jealousy---if they feel that the glamor of aspiring to a ToE, "realizing Einstein's dream", is their turf. If they felt that G.L. was infringing on public attention that was rightfully theirs. Maybe some string theorists feel that any sign of competition is an outrage and should be crushed.

But the outrage I heard in the science blogs didn't just come from envious or defensive string theorists. I think it contained a kind of puritanism and desire of some to control public reaction---a sense that publicity (especially when it gets out of their control) is somehow bad. Somehow G.L.'s infant theory was being given a whipping because it had made a media splash and that was BAD. It was out of control and it was a no-no.

I don't really understand but it seems to me that science blog-owners may think that they should be the gatekeepers and regulators of public attention.
Also the prominent ones are a new type of media personality. A little bit like science "talk show hosts". They have a kind of power. And that means that when things get out of control or where there is an issue of control, then the APPARENT issues (e.g. the degree of incompleteness of a new theory, the prospects for constructive revision, whether inconsistencies are fixable or fatal etc.) may not be what all the animosity is about. It may actually be more about issues of power.

Then there's the issue of conformity. Science is a community function that requires a balance of conformity and individuality. when the chips are down conformity has to win, and the ultimate sanction is ostracism. Ultimately the survival of the community trumps all other considerations. So that instinctive reflex has to be taken into account as well.

All in all, quite a fracas! Even you might call it a kind of minor street-riot.

====EDIT====
I wanted to include this valuable quote from S. Hossenfelder, because I strongly agree with almost everything said here and it is said very well and clearly, for the most part:
==quote Hossenfelder==
The hype of science in the media just reflects a general trend caused by information overflow. In today's world you have to scream really loud to be heard at all, and headlines are the better the fatter. I generally dislike this, as it leads to inaccurate reporting, unnecessary confusion, and bubbles of nothing. All of which obscures sensible discussions and is a huge waste of time.

However, despite this general trend, what worries me specifically about popular science reporting is how much our community seems to pay attention to it. This is a very unhealthy development. The opinion making process in science should not be affected by popular opinions. It should not be relevant whether somebody makes for a good story in the media, or whether he or she neglects advertising himself. What concerns me is not so much the media re-re-repeating fabulous sentences, but how many physicists get upset about it. This clearly indicates that they think this public discussion is relevant, and this should not be the case.

Concerns about the public opinion arise from the fear it might affect the funding of some research areas. But it's not the media who creates fashions and hypes who is to blame. Neither is it the scientists who are not careful enough when talking to journalists who are to blame. To blame is everybody who tolerates that the funding in science is subject to irrelevant factors.
==endquote==

The boldface emphasis is in the original. There is some ambiguity. They should not think that the public discussion is relevant? (Because publicity does not affect the judgement of the agencies.) Or their fears are justified and indeed publicity affects the funding agencies and THIS should not be the case.

the last sentence may require some clarification, is it really true (as some people fear) that irrelevant factors do---and if so what factors. my impression was an oldboygirl network based on prestige and influence entirely within the community and there is some politics sure, but it is not public politics.

But on the whole, apart from some ambiguity, I agree very much with the middle paragraph---and include the rest for context.

10st1denTT

Nov26-07, 12:51 PM

just want to pay you a compliment on the pithy way you sum things up.
//...//
Hope you keep striving towards conventional understandability, because you have something to say to us((my bold)).

Thanks marcus,
I think that was the kind of welcome on a board that anybody would wish for! In contrast to your last statement, i am somewhat sceptical though. I was mainly lured here by noticing that John Baez and Garrett Lisi had been dialoging here prior to the release of his now famous (read with a neutral tone) paper. My personal expertise on the matter at hand is Not deep. And my presents here is more about recieving than giving! I am well aware that you have been closely involved in the discussions of Lisi's ideas (dating back till 2005!). And i feel honoured to conversing with you now...
My ambition reaches not further than to abstain from disgracing these pages with too much stupidity. (My hope is that the "Lisi-ToE" was a valuable contribution (at least) and that the polemics around it will quiet down.)...

//(a child demands my attention :))

marcus

Nov26-07, 02:56 PM

Hi Lost I.

I thought my initial response was immodestly cordial so I toned it down, in edit. But I am glad you saw and copied!

There is something that is more on-topic that concerns me a lot now, and I want to raise.

For several days I have had the suspicion that G.L. project of an E8 theory runs into trouble in part because it is not based on deSitter general relativity.

I have been reading Pereira etal paper 0711.2274 "de Sitter Relativity: a new road..." and trying to understand it.
It has a new form of Einstein's strong equivalence principle (that invokes deS local ambiances rather than the conventional Minkowski ones) and a new form of the Einstein field equation.

I keep struggling to understand the paper, and also why it is not picking up more notice. These guys are not nuts. They are top people by Brazil standards, at the Sao Paolo Institute for Theoretical Physics.
If you are going to unify QM with GR, then what General Relativity do you unify it with?

The conventional Minkowski space doesnt expand. deS space does. In a world with a positive cosmological constant it might be more realistic to work with a form of GR that is locally deS rather than locally Minkowski

So I have been expecting that if Garrett's approach is a good one then at a certain point someone will have a flash of insight and say "Wait! This fits better with deSitter General Relativity!" And then (if the approach is an overall good one) some of the kinks will get worked out, or so I have been imagining.

This is a dim hunch that you don't usually tell people.

10st1denTT

Nov26-07, 03:49 PM

"subtle is the Lord"

In the end there will be a higher authority than the presently reigning DemiGods, that decides which fundamental theory is simply right and which one is Gloriously FALSE!
Somewhere in the basic foundations of reality there Must be beauty and (a kind of!) simplicity. There Must be logical consistency. And there Must be an answer to the question: Why had Everything to be the way it would?
Every once in a while there Will come an Individual who thinks deeper, abstracts more efficently (the bones from the flesh) and finally goes one step Further (for the mainstream to follow).
It's about time such a "Ferguson" showed up (flying in on a second hand kite or what ever!).
If Nature would be as intricate/convoluted/traversed/outre´/... as the string theoreticians figure, she would trip over her own TOEs at every single instance!
I think, however bad the state of morals in physics, there is enough space under the feet of the bestriding giants for a Ferguson to grow, thrive and bloom. (I think btw that she is sitting in a cold spartan room with a spartan bed and a raw spartan kitchen table and a lot of the Right books - and only a little, shabby computer- Right Now! - talking to herself, the physicists/mathematicians (alive or dead) from her books and to some Imagined/Fancied Higher Being also!)

((ExpectTheUnexpected))

10st1denTT

Nov26-07, 04:12 PM

(this is going to be a funny game :) , we are seriously out of sync, isntit)
((i accomodate any style bytheby if i have the impression of a likable soul on the other side))
to your last post: I am a trained mathematician and conditioned to talk only things, i understand at least in their basic workings. You are presently talking over my head! I find the Lisi idea promising to think the Einstein world anew (demote the metric, think "connection"). I am just beginning to study MM. As I said, I am here to Learn!

marcus

Nov26-07, 07:03 PM

The basic object in LQG is the SPIN NETWORK. Conceptually the spin network can be thought of as dual to the connection* idea. It only involves a finite (or sometimes countable) number of vertices, while a connection is defined over the whole continuum.
But it does give you information about what happens when you pass from one point to the other. Spin networks and connections are kindred ideas.

In LQG, quantum states of spatial geometry are described by spinnetworks. But so far only geometry is described by them, not matter. Matter fields can be stuck on, but they don't come free as part of the spinnet.

Lee Smolin's research group is embarked on trying to realize the standard particles of matter as TWISTS AND BRAIDS in spin networks. It is a risky and difficult venture. They have to show that patterns of braiding can propagate without getting unravelled, and that their interactions correspond to the known interactions of particles.

Twists and braids (in a network of tubes or wires) could turn out to be dual to a more complicated type of connection----analogous to how ordinary spinnet (without twists and braids) is dual to a simple geometrical connection.

Twists and braids are ALGEBRAIC things in the sense that you can combine them (doing two braids in sequence gives you a new braid) and sometimes one will UN-do another.

I have to go, and don't have time to finish this thought. What I am driving at is that realizing the standar particles as twists and braids in a network as you go from one point to another could be akin to realizing the same particles in the Lie group of a connection. Each could provide helpful guidance for the other. This would be a fabulous duality, especially since the way is difficult on each side.

*What is a connection? In ordinary differential geometry a connection specifies a way for tangent directions to change as you travel from one point to a neighboring one---a connection defined on a shapeless continuum can give it geometric shape just as well as defining a distance function (or metric) on it can. If defining the shape of a continuum by specifying a metric on it is the usual way, the practice of defining it with a connection is not far behind.

10st1denTT

Nov27-07, 08:06 AM

I would simply like to add that i whole heartedly subscribe to your observances in post #152.
BTW, what irritated me in your post #154 was the passus

"it might be more realistic to work with a form of GR that is locally deS rather than locally Minkowski"

i thought i had learned from the (quite excellent) thread on SO(4,1) here on PF that "deS" (meant to be read deesse?) was locally Minkowski Anyway(!) (in perfect accord with what we know about space expansion and what we see in our labs)... Maybe i should have a look on that Pereira paper (ififindthetime:))

jal

Nov27-07, 01:18 PM

How will E8 be tested?
3. Dynamics
The dynamics of a connection is specified by the action functional, S[ : A]. Classically, extremizing this action, constrained by boundary data, determines the value of the connection, : A(x), over a region of the base manifold. The value of the connection may also be used to infer topological properties of the base manifold. Quantum mechanically, the action of a connection over the base manifold determines the probability of experiencing that connection.[15] Since quantum mechanics is fundamental to our universe, it may be more direct to describe a set of quantum connections as a spin foam, with states described as a spin network. Under more conventional circumstances, the extensive methods of quantum field theory for a non-abelian gauge field may be employed, with propagators and interactions determined by the action.
In any case, the dynamics depends on the action, and the action depends on the curvature of the connection.
… It should be emphasized that the connection (3.1) comprises all fields over the four
dimensional base manifold. There are no other fields required to match the fields of the
standard model and gravity.
…The theory proposed in this paper represents a comprehensive unification program, describing all fields of the standard model and gravity as parts of a uniquely beautiful mathematical structure. The principal bundle connection and its curvature describe how the E8 manifold twists and turns over spacetime, reproducing all known fields and dynamics through pure geometry.
Everyone has their special model that they are working on and I assume, that is what they will be using to evaluate E8.
They will be looking at E8 to determine if their model is represented and will arrive at one of the following conclusions.

1. Yes, …. My model fits, therefore, E8 could be right.
2. No, …. My model does not fit in, therefore, E8 must be wrong.
3. Maybe, …. My model does not have or need all of the connections shown.
4. Maybe, …. My model needs more connections then what is shown by E8.

Then I expect that the next phase will be,
1. E8 says that it’s there but we cannot locate it in the noise.
2. My model says it’s there but we cannot locate in the noise.
--------
As a concrete example;
What would the following authors conclude?
http://arxiv.org/abs/0711.3910
SU(6), Triquark states, and the pentaquark
----------
jal

cyberiantiger

Nov27-07, 06:39 PM

I love the theory, though "simple" is perhaps not a word I would choose to describe it.

I confess that my maths probably isn't up to understanding it yet, it seems that I really need to understand octonions and lie groups in order to get a real handle on this theory (I dropped maths 2 years into a university course for reasons I won't go into).

The majority of reviews on science blogs which tear the theory down for one reason or another are mostly flawed and if one reads around you can find alternative reviews which point out the same flaws (except for the one I read which claimed you couldn't add different types of quantity together - where the paper was quite obviously talking about vector maths and not actually adding different types of quantity together) but then added that though there were flaws they could be worked around. I gather that some of these blogs are owned by respected scientists, and I find this quite disturbing.

With regards to the mass media attention, I think it's probably done the theory more good than harm; Alternative theories historically have also initially suffered the same sort of acceptance by mainstream science, it's a shame mainstream science never learned the lesson that theories should be accepted solely on their ability to be proven or disproved.

The best summary I can see is that the paper is an incomplete alternative way of approaching solving some fundamental physics questions which string theory tried to address and mostly failed (Anything which by definition cannot be proven is a religion NOT science).

I will hopefully be spending some of my spare time trying to understand octonions, Lie groups and eventually E8, then I will reread the paper and hopefully understand the finer details and then unfortunately I will have to catch up my physics from a long way behind where it needs to be in order to start trying to apply this theory to anything meaningful.

Meanwhile I'll be sure to be keeping tabs on anything related to this topic, especially this thread.

The theory perhaps strikes a cord with me because what little physics I did led me to believe that there were probably 2 more forces on top of the standard 4 forces I learnt about, mainly for reasons of symmetry with the fundamental particles. Well below the level this thread is at, did I mention my physics sucks ?

I suspect the theory will become more beautiful as I understand more about e8 and the Lie Groups, I also suspect the theory will become more flawed as I understand more about the physics side of it though ;)

Sorry for the long post, hopefully I'll have something more useful to contribute if I ever managed to catch up to the level this thread is at.

Count Iblis

Nov27-07, 07:47 PM

In the interests of balance, we should probably point out that Lubos has savaged the paper.

What a surprise! A nice parody on Lubos' blog (http://insti.physics.sunysb.edu/~siegel/parodies/atchoo.html) :smile:

Coin

Nov27-07, 10:49 PM

I love the theory, though "simple" is perhaps not a word I would choose to describe it.
The title was a pun. E8 is an Exceptional Simple Lie Group.

I will give you a few minutes to stop groaning

marcus

Nov27-07, 11:39 PM

The title was a pun. E8 is an Exceptional Simple Lie Group.

I will give you a few minutes to stop groaning

Yes! and puns aside, this might be a place to cover a few essentials of group theory (counting on Coin's help)

a simple group is sortofanalogous to a prime number in that you can't factor out any subgroup and collapse it down any further.
a simple group is one that contains no subgroup of a type that lends itself to factoring out (called a normal subgroup)
(like a prime number doesnt contain any factor you can divide by to make it smaller)

If the group can't be simplified that way, it is called simple (even if it's highly intricate, because it is already as simple as you can make it without totally trashing it).
=======================

Actually the source of Garrett's beautiful diagrams of E8 is another special kind of subgroup called a maximal abelian subgroup, or Cartan subgroup. A Cartan subgroup for E8 is 8 dimensional. that is the basic reason that all Garrett's E8 diagrams exist in 8D.
The Cartan subgroup is an easy concept to grasp and it's the key to how the larger group's structure is analyzed.

If anyone is curious about it, just ask. Coin, or myself, or half a dozen other people visiting PF Beyond forum these days, could possibly explain.

More difficult ideas, I personally don't make any guarantees or promises. But the Cartan subgroup is a babystep idea---and it's amazing how much structure it unlocks.

dipstik

Nov28-07, 10:45 AM

please explain the cartan subgroup.

-thanks

marcus

Nov28-07, 02:56 PM

I'd be happy if some of the others want to take over. But you know what a group is. If you know matrix multiplication you can think of a group of matrices----or pick up a book and think of the different ways to flip it, turn it etc.
Especially if it is square so there are more possible moves (i.e. symmetries. )

You can experiment with groups and find that not all moves commute.

But in any group you can find subgroups (even if it is only the trivial subgroup consisting of the identity) and in any group you can always find one or more commutative subgroups.

Like pick one element, and square it, and keep on multiplying it by itself. At least in a finite group that looks like it would generate a subgroup that is all commutative. Correct me if I'm wrong, or ask questions if you don't follow.

So you can start with one element and its powers (square, cube..) and you can keep picking other elements and trying to see if they commute with what you already have. So you can keep adding more and more and building up the subgroup until you have a maximal commutative subgroup. That means you can't add any more. Any other element you try will not commute with some element you already have.

It's like the maximal bunch of friends you can invite all to the same party at your house. So to sum up:

1. Not all groups are commutative. In some (like even the symmetries of a square) you find a pair of elements that it matters in which order you do them.

2. All groups have subgroups

3. Any group has at least one commutative subgroup.

4. At least under reasonable assumptions, I'd expect a group to have a maximal commutative subgroup.
================

That is basically what a Cartan subgroup is. now you can ask all kinds of questions like is it UNIQUE in some sense.
If you started building a commutative subgroup with different initial choices whould you get something that was at least the same size?
Questions of the sort mathematicians love to ask. dont let these intriguing questions distract us from the basic fact that we are talking about a very simple concept.

And another question is what about INFINITE groups, or what if the group is a continuum. A smooth manifold of a certain dimensionality----like 1, or 2, or 248.
Then what does maximal mean? And you want to know what the DIMENSION of the subgroup is, because you cant count discrete elements any more. And you want to know if maximal commutative subgroups are unique in what sense? At least they should have the same dimension.

Several other people are doubtless more familiar with this and could continue the discussion. my impulse is to consult Wikipedia on Cartan subgroups at this juncture.

But anyway to conclude this intro, E8 has a maximal commutative subgroup of dimension 8.
The whole group is a manifold of dimension 248. And it is not very commutative. But you can find a commutative subgroups of dimension 8.

And that turns out to be cool because you can then study how the small 8d subgroup ACTS on the group at large and....=====but OOPS! at this point we have to say what is a LIE ALGEBRA.
Groups that are manifolds are nice to study because a manifold has a tangent space at every point and if it is a group then it has a tangent space at the identity which the groups own multiplication projects a nice bit of algebra onto, making the tangent vectors at the identity into an algebra.

And then the Cartan subthing is going to act on the thing as a whole and it's linear (vectors, now) so there are going to be eigenvectors and eigenvalues====matrix stuff that you normally get a math package to do, but which is extremely useful.

If want to proceed, ask something. Then maybe somebody else besides me will take a turn.

=========EDIT TO REPLY TO NEXT============

Coin thanks! First of all for not leaving me dangling. Also for clarifying. And what you say is basically right
So the cartan subgroup of E8 would just be the largest subgroup wherein the lie bracket is everywhere 0? Is that right?
Right! (im not an authority but I would say largest subalgebra of e8 wherein the bracket is zero.------or the largest subgroup of E8 wherein ab = ba)

a useful confusion exists between a Lie group and its algebra---as between a diff manifold and its tangent space. one is linear with vectors you can add, and one isnt but they are intuitively much the same thing and should be thot of in the same mental breath :-)

To be circumspect about it, the only added complication here is keeping track of when we are talking about the group E8 and when we are talking about its Lie algebra, the tangentspace at the identity that has the bracket defined. that would normally be called e8. they tend to use caps for the group and lowercase for the algebra. but the two are so closely related that people often don't distinguish carefully and write E8 for the algebra as well as for the underlying group.

Coin

Nov28-07, 03:24 PM

william donnelly

Nov29-07, 05:39 PM

Coin, you're getting closer, but you are confusing E8 (the Lie group) with e8 (its Lie algebra).

E8, the Lie group is a 248 dimensional manifold. It has a multiplication that is NOT always commutative. i.e. a*b != b*a.

e8, the Lie algebra is the 248 dimensional tangent space of E8. It has an addition, and addition is always commutative. It has a Lie bracket that is not necessarily zero, [a,b] != 0.

Sitting inside E8 is the Cartan subgroup, which is 8 dimensional and commutative. It's shaped like an 8-dimensional torus. It's a maximal Abelian subgroup, in the sense that there is no bigger Abelian subgroup that contains the Cartan subgroup.

Sitting inside e8 is the Cartan subalgebra, which is 8 dimensional. The Cartan subalgebra is the tangent space of the Cartan subgroup. It has a Lie bracket that is always zero.

Coin

Nov29-07, 09:23 PM

William, thanks! While I have your attention, do you think you could maybe offer any help with my questions from page 8?:

From looking at wikipedia (http://en.wikipedia.org/wiki/E8_%28mathematics%29#E8_root_system) and this page (http://aimath.org/E8/e8.html) (I think from the "atlas" people who "mapped" E8 awhile back?), the impression I get is that E8 consists of those vectors of length 8 that can be formed from adding together integral multiples of the members of a basis of "root" vectors. The group operation appears to be vector addition, and the "root" vectors consist of all 8-member vectors of the form
<±1, ±1, 0, 0, 0, 0, 0, 0>
or
<±0.5, ±0.5, ±0.5, ±0.5, ±0.5, ±0.5, ±0.5, ±0.5>
Because there are 8-vectors which it is not possible to construct by adding together these roots, E8 forms a proper subset of the set of {all 8-member vectors consisting of integer or half-integer values}.

Is all this correct? Okay, so: If so, is this the E8 Lie group or the Lie algebra? In either case, what is the corresponding algebra/group? And in the case of the algebra, what is the lie bracket? (The atlas page says only that the lie bracket for E8 is "very hard to write down". Oh.) And finally, is it "weird" that E8 is a lie group/algebra-- yet has only a countably infinite number of members, and is apparently constructed entirely of discrete structures? I've thus far only encountered lie groups which are continuous, where it makes sense to talk about things like "infinitesimal generators". There doesn't seem to be anything infinitesimal about E8 at all. (Mind you, I'm not complaining-- I have a CS background and I am WAY more comfortable with anything discrete than I am with anything continuous! It just seems jarringly different from the way I understood people to use lie groups/algebras previously, and I'm confused how I missed this.)

Past this, the biggest thing that is confusing me here are the "roots". First off, although this is probably not all that important, how on earth were they chosen? That is to say, was someone just playing around with addition on different sets of basis vectors, and went "oh hey this particular combination of 248 vectors acts kinda weird, everyone else come look at this"? Or was E8 first discovered as some other kind of structure, and it was later realized that the 8-vectors above are a convenient representation of that structure? Second off and more importantly, I am dreadfully confused by these root "diagrams" such as one finds all over Lisi's paper. As far as I can tell, the idea is that we plot each of the roots as a point in eight-dimensional space. (I take it that we plot them by simply treating each 8-vector as a coordinate?) However, then we for some reason draw lines between some of the roots! Why on earth do we do this? What do the lines mean?

I'm similarly a little bit confused by this "simple root" thing that wikipedia describes. As far as I can tell, the "simple root"s are an alternate integral basis for E8, consisting of the eight vectors found in the rows of this matrix:

http://upload.wikimedia.org/math/7/5/b/75bce2aa3f595732bd54baa61e503070.png

Wow, that's convenient! What's confusing me here though is, why on earth do we bother using the 248 roots described above, when we could just use these 8 simple roots and be done with it? Another thing confusing me: Wikipedia offers a "dynkin diagram" (which I take it is different from the "root diagrams" used with the 248-root system) which looks very deep and beautiful:

http://upload.wikimedia.org/wikipedia/en/d/d3/Dynkin_diagram_E8.png

... but I can't for the life of me figure out what it's supposed to mean. Wikipedia says that this is a graph where vertices represent members of the simple root system, and edges are drawn between any two members of the simple root system (I assume this means a 120 degree angle when we treat the simple roots as coordinates in 8-space.) Okay, that's nice, but why? Why do we care which members of the simple root system are at 120 degree angles to one another?

I have a couple more questions related to what Garrett in specific is doing, but these are just my questions about the E8 [group? algebra?] itself. Any help in figuring these things out would be appreciated. In the meanwhile, something vaguely frustrating me is that there does not seem to be any specific information on E8 in the obvious places. It is clearly a well-researched subject but the best I can find is these very vague wikipedia-style summaries, and John Baez's writeups (which are invariably exhaustive and lucid, but everything I've found which Baez has written covering E8 seems to be primarily about other things, like octonions, and only indirectly concerned with E8). Is there some particular thing, perhaps a book, I would be best served by going and reading if I am curious about the mathematics of E8?
I take it from your comments that the 8-vector w/addition I describe above is the lie algebra. If this is the construction for the lie algebra, how are the members of the lie group constructed? And how do you find the members of the Cartan subgroup of the e8 lie group?

william donnelly

Nov30-07, 07:22 PM

This 8d space is _a_ Lie algebra, but it's not the e8 Lie algebra, it's the Cartan subalgebra. The set of 240 8-dimensional vectors described in the link is the E8 root system, which lives inside the Cartan subalgebra.

Actually constructing the Lie group E8 is apparently quite complicated, and I have no idea how to do it. John Baez talks about it in TWF 253: http://math.ucr.edu/home/baez/week253.html.

To find the Cartan subgroup, one thing you can prove is that the Cartan subgroup has a single vector, that when you take all multiples of this vector you can recover the whole Cartan subgroup. So if you can find this one vector, you get the whole Cartan subgroup. I'm not sure how you would get this vector though, other than by just trying all of vectors.

rntsai

Nov30-07, 11:32 PM

There's a standard way to label the 240 roots in Table 9
of Lisi's paper as weights of the adjoint rep of e8.
The rep is 248 dimensional; it has a weight [0,0,0,0,0,0,0,0]
with multiplicity 8 that corresponds to the cartan subalgebra.
The remaining 240 weights have multiplicty 1 and can be listed as :

[ [ 0, 0, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 0, 0, 0, -1 ],
[ 0, 0, 0, 0, 0, 0, 1, -1 ],
[ 0, 0, 0, 0, 0, 0, -1, 1 ],
[ 0, 0, 0, 0, 0, 1, -1, 0 ],

... <deleted 230 of 240 nonzero weights>

[ 1, 0, -1, 0, 0, 1, -1, 0 ],
[ -1, 0, 1, 0, 0, 0, -1, 1 ],
[ 1, 0, -1, 0, 0, 0, 1, -1 ],
[ -1, 0, 1, 0, 0, 0, 0, -1 ],
[ 1, 0, -1, 0, 0, 0, 0, 1 ] ]

so each "particle" is represented by 8 integer values.
Actually it looks like only (-2,-1,0,1,2) occur in the list.
This representation is different from the coordinates
of the polytope mentioned in the paper.

Table 9 includes 8 labels :

(1/2i)w_T^3,(1/2)w_S^3,U^3,V^3,w,x,y,z

These are probably more physically meaningful than the
above integral weights. There should be a map between the
two which would be good to have explicitely worked out.

Unbeliever

Dec1-07, 06:35 PM

Even if Dr. Lisi's model turns out to be other than the long-sought TOE - if it merely points others in fruitful directions - it will have performed its appointed task, and have followed Galileo's Dictum, and contributed to science. And, who knows, maybe we're all in at the ground floor of historic science! I, for one, am happy to be so close to the edge of the envelope of the search for knowledge. I'm not by any means a physicist, only an interested layman, but I enjoy being here. Thanks for having such a fun discussion!

marcus

Dec1-07, 10:34 PM

Even if Dr. Lisi's model turns out to be other than the long-sought TOE - if it merely points others in fruitful directions - it will have performed its appointed task, and have followed Galileo's Dictum, and contributed to science...

I share your attitude. Win or lose, a testable theory---one that makes new predictions that can be checked---can help advance understanding. especially if it stirs people up and gives them ideas of things to try and not try.

At the moment I can't think what Galileo's dictum might be. Can someone help me out?
I thought the programme of empirical science was laid out by Francis Bacon, early 1600s. A contemporary of Shakespeare and an early martyr to the frozen food business.
(he died after an unfortunate experience with a chicken.)
============================

Online conversation between two science writers: George Johnson and John Horgan
discussing AESTOE among other things
http://bloggingheads.tv/video.php?id=471

the first two minutes is about Horgan's list of the 70 greatest science books, but then they get into a 14 minute discussion of E8 and events surrounding its arrival on the scene. Savvy science journalists, especially George Johnson IMO. They made some astute comment on the academic and media reaction. Then they got on to other (most likely sillier) science stories of the past week.

Unbeliever

Dec2-07, 04:17 PM

At the moment I can't think what Galileo's dictum might be. Can someone help me out?

I got that from Bertolt Brecht's, The Life of Galileo:
Science knows only one commandment: contribute to science.
I read somewhere else that this is known as Galileo's Dictum.

marcus

Dec2-07, 05:07 PM

Brecht deserves a lot of respect as a playwright and it is a good dictum.
But there may be two famous Galileo dicta. I googled and found this other saying that the universe is a great book:

"this grand book . . . is written in the language of mathematics, and its characters are triangles, circles, and other geometrical figures."

http://findarticles.com/p/articles/mi_m0425/is_n1_v55/ai_18299591/pg_3

and something like that in Italian
Per Galileo l'universo è un libro, il «grandissimo libro che continuamente ci sta aperto innanzi agli occhi …, ma non si può intendere se prima non s'impara a inteder la lingua, e conoscer i caratteri, ne' quali è scritto. Egli è scritto in lingua matematica, e i caratteri sono triangoli, cerchi, ed altre figure geometriche, senza i quali mezzi è impossibile a intenderne umanamente parola».
http://www.italialibri.net/arretratis/apr00.html
This has the same quote and also a great quote from Johannes Kepler.
http://www.phyast.pitt.edu/~micheles/notabili.html
The Italian Wikipedia begins its Galileo article with this same quote
http://it.wikipedia.org/wiki/Galileo_Galilei

arivero

Dec2-07, 06:42 PM

A secondary reference is a kind of paperback answer to Horgan's "End of Science" (I guess it because it was contemporary and the editors used the same format and cover colours; it could be reverse, or unrelated)

http://www.amazon.com/GALILEOS-COMMANDMENT-ANTHOLOGY-SCIENCE-WRITING/dp/0316648280/ref=sr_1_1?ie=UTF8&s=books&qid=1196641527&sr=1-1
http://www.amazon.com/gp/product/0805073493/ref=cm_cr_pr_product_top

The Amazon review of this book contains Brecht's reference. It is taken from the second page of the introduction, and then again from the first quote in first part of the book. So it comes, in some sense, from the editor, Edmund Blair (is he related to Eric Blair, or is it a very common name in England?).

If I were to abstract Brecht to a single quote, it could be
“Of all the days that was the one /
An age of reason could have begun”
But note this is also reductionist; to get an idea of Brecht's arguments, one should at least to read the whole speech of Galileo to Viviani in the last act, if not the whole work with some dense introduction about the text.

jal

Dec4-07, 12:06 PM

I would like to keep "An Exceptionally Technical Discussion of AESToE" in this forum so that the non-math people (laypeople and amateurs) could ask questions in the adjoining threads.
Maybe we'll get explanations maybe not from Garrett and others.
jal

marcus

Dec4-07, 06:16 PM

Garrett, here is a not-very-technical somewhat vague question, in case you have time to consider a few of those as well.
BTW thanks for coming around some and helping us understand your work! I wish more researchers did that!

My question is how would you see E8 theory adapting if a deSitter General Relativity emerged and began attracting interest, say along the lines of
http://arxiv.org/abs/0711.2274
?

You may immediately see some reason that Pereira Aldrovandi deS-GR is doomed, flakey or flimsy, in which case the question doesn't matter. Or you may not have time to look at the P&A paper, in which case the question isn't useful and can be ingored. Basically what they do is replace the Poincaré group in the strong equivalence principle by the deS group and get a new version of the Einstein Field Equation with a new term on the RHS. Their equation (27).

This kind of thing could be dime-for-a-dozen or necessarily inconsisitent, but so far I've seen no evidence of that and I find the idea hard to shake.

what if it turned out that the proper local spacetime symmetry group to use was NOT the Poincaré, suppose the right group was SO(4,1)?

If the right group turned out to be SO(4,1), then where would E8 theory be, and how would it adapt? Can you say anything about this, without getting too distracted from your main focus?

garrett

Dec4-07, 07:20 PM

Hey Marcus,
I can reply with a vague answer. The E8 theory so far includes a so(7,1) symmetry, which breaks up into so(3,1)+so(4) +4 \times 4. The first 4 is the gravitational frame, and the second 4 is the Higgs. When the Higgs gets a VEV, there is sort-of a so(4,1) symmetry because of so(4,1) = so(3,1) + 4. So the theory includes so(4,1) and is compatible with De Sitter gravity this way. But things are more confusing because of the inclusion of the Higgs.

Nuha

Dec5-07, 09:09 AM

Sorry for poor English.

"An Exceptionally Simple Theory of Everything" is not Theory.
I agree with that that is in its basis. This big achievement!
Respect to the authors.

But.
This is just perfect Mathematical method and modell.

It is a part of the another theory.

"Information fields and their interaction with multivariate coordinate space-time in conformity with the discrete nature of mother"

The discussion is in Russian Phisycs phorum (about 2 month).
(Moscow State University)

The key formula and another information is hear.
Sorry but i'v a problem to translate it in English.

http://forum.dubinushka.ru/index.php?s=&showtopic=12456&view=findpost&p=352715

rot(G*Kg) = n*Kn + rot(H*Kh) + rot(E*Ke)

Metricss of the validity are deduced.
Connecting parities.

Unbeliever

Dec7-07, 07:12 PM

I hope this question hasn't been covered yet, I don't have time to read this whole thread. I'm curious about the 20 new particles that the theory predicts: must we wait for the LHC to come on-line, or can any of them be gotten at existing facilities, with current energies?

BryanP

Dec7-07, 09:11 PM

Thanks, just printed it.

polystethylene

Dec8-07, 09:32 AM

As a fourth year masters student just starting to learn about symmetry groups and unification and the like, this is something of an eye-opener, in that I have no idea what's going on in this paper. From what I can gather from the sections of prose though, it seems like a pretty beautiful and simple theory, congratulations garrett.

Valjean

Dec9-07, 11:25 AM

And just maybe...to get to the fundemental condition that everything is based on...attraction exists between everything. Its strength between any two things, in any given circumstances, depends exactly on the amount of mass involved. So exact that the source of that attraction must be a the smallest, indivisible bit of mass there is. To have the same result you have to have the same ingredients. Some of those bits collect, because of the attraction, into units and others orbit around them in regular frequencies and amplitudes. As those motions cause any given two bits to move closer and further relative to each other the attraction between them increases and decreases accordingly. Energy frequencies of attraction that travel outward until they meet another bit causing its orbit to alter ever so slightly but still altered...maybe even a bit inside your eye which passes to the next, etc. So, how might that attraction exist? Consider. Nothing. Starting from the same place as the bang, formation of strings, etc. a separation, a compression of space into one bit of compressed space surrounded by expanded space created by the same action, like a teeter-totter, which then "banged" causing it to shatter into countless bits each still surrounded by the expanded. space. Or maybe there was just a crystalization producing the same thing in one action. Maybe a bad example but...a solid rubber ball. Draw rubber into points of compressed rubber each surrounded by expanded rubber pulling any two compressed points towards each other but can't move them because of the equality of pull between all of them. Move one, however, and a never ending dance starts because of the ineaquality of pull aka attraction. Back to the bits. Some compressed points (energy) our instruments can detect that we view as matter. Others don't. Dark matter? We don't detect it but it still has its attraction basis. We don't detect the expanded space (energy) as such but it is a necessary component for attraction to exist. We detect the results of its being but not it directly. Dark Energy? Or maybe it's all hogwash.

timex

Dec9-07, 06:18 PM

Where is time in the theory?

rntsai

Dec10-07, 04:18 PM

Where is time in the theory?

timex,
I think time translation corresponds to one of the generators of one the two
d4 subalgebras; which one I haven't figured out myself yet. The d4 corresponds
to an so(8) (or so(1,7) or so(2,6)); I think somewhere in these so's there's
an so(2,4) related to the poincare algebra; time translation is one of the
15 generators of this so(2,4); x,y,and z translations are another 3,...
My understanding of this at this point is very vague and possible wrong,
but maybe someone can clarify.

Denton

Dec15-07, 07:20 AM

I really wish I could understand this... its just currently out of reach.

marcus

Dec19-07, 02:56 PM

On 6 December Smolin posted this paper, and then entered discussion at the blog Cosmic Variance (where content-free insults by anonymous posters are permitted)

http://arxiv.org/abs/0712.0977
The Plebanski action extended to a unification of gravity and Yang-Mills theory
Lee Smolin
13 pages, one figure
(Submitted on 6 Dec 2007)

"We study a unification of gravity with Yang-Mills fields based on a simple extension of the Plebanski action to a Lie group G which contains the local lorentz group. The Coleman-Mandula theorem is avoided because the theory necessarily has a non-zero cosmological constant and the dynamics has no global spacetime symmetry. This may be applied to Lisi's proposal of an E8 unified theory, giving a fully E8 invariant action. The extended form of the Plebanski action suggests a new class of spin foam models."

==================
Two things are especially notable. On one hand, Smolin together with several others (Wan, Hackett, Kauffman, Bilson-Thompson...) is currently working on an entirely different LQG unification program----a scheme for merging matter with geometry that COMPETES with Garrett Lisi's E8 approach. It uses topological features such as twists and braids in the network to represent matter and attempts to realize the standard menu of particles.

On the other hand, in Smolin's paper he offers a second level of competition. Because he proposes to go partway with Lisi but (1) allow for using a different group from E8 should that turn out necessary and (2) realize fermions in a radically different way from how Lisi goes.

So Smolin is offering two competing unification approaches, one which looks somewhat Lisi-like and another (involving more collaborators) which is completely different. I think the aim is to get ideas out there where they can be examined and discussed, presumably in a professional way, and perhaps further modified. The game being not to win arguments or score points but to see if any variations of these ideas could be worth pursuing---maybe even right.

So then that was 6 December and then there was the discussion at CV blog presided over by Sean Carroll. that may have now burnt out and be more or less over. not sure but maybe. have to go, back later

Lee seems to have stated his conclusions from the discussion in the form of a long post, which is an interesting document in itself.
http://cosmicvariance.com/2007/11/16/garrett-lisis-theory-of-everything/#comment-306890
It comments on the blog-context as well as the physics content of the discussion in that CV thread.

One thing that seems very obvious but which no one has remarked on, is that in TRADITIONAL pre-blog scholarly discussion, as soon as Smolin posted his paper (Arxiv 0712.0977) responding to, utilizing, and diverging from Lisi's. Then the obvious thing to do would be for Distler to post a critical response IN THE FORM OF A SCHOLARLY PAPER ALSO ON ARXIV. Traditional scholars do this all the time---they post papers with titles like Comment on "The Plebanski Action Extended to a Unification..."
I have seen dozens of such papers. Sometimes they are published. Sometimes they are replied to with yet another scholarly paper by the original authors!

The advantage is that in an exchange of papers each person assumes responsibility for what they say and has the job of saying it clearly and carefully. Then anyone who is interested can see what each actually said and how they addressed each other's points.
By contrast in a series of BLOG COMMENTS it is very difficult to find and keep track of what people are actually saying because it is mixed in with a lot of anonymous trash and side-discussions. Blog commenters may also use innuendo or careless suggestive language because no one is being held accountable in the way they are with professional journal article format (footnotes, references, point-by-point organization that one can inspect and judge for clarity)

So there really is some merit to the classic way scholarly debate is organized and the classic journal article style. If anybody habitually avoids that format and seems to PREFER the more disorderly, time-consuming, and irresponsible Blog medium----if they have the professional status ensuring ready visibility on arxiv----then to me it seems questionable. I wonder why they insist on Blog-wallow when they could easily and clearly get their message across on HEP-TH.

ccdantas

Dec19-07, 04:26 PM

mitchell porter

Dec19-07, 06:12 PM

I wonder why they insist on Blog-wallow when they could easily and clearly get their message across on HEP-TH.

It may yet happen. But most of the blog discussion is ultimately a reaction to the mass media coverage of Lisi's original paper (except for Lubos Motl's post, which I think was an immediate earnest reaction to what he regarded as an absurd paper). There might have been one or two brief "comments", saying exactly what people have been saying on the blogs. Or it might have been ignored outside of LQG. As someone wrote at Wikipedia, "I don't think anyone here realizes how many wrong papers are posted on that preprint server every day. No researcher has time to debunk them - it would be a completely thankless and Sisyphean exercise. Instead, they just get ignored."

You could compare this case to Joy Christian's paper, earlier in the year, claiming a counterexample to Bell's theorem. That has received about half a dozen rebuttals at the arxiv, and no blogosphere flamefest. But even that paper was in New Scientist, so one cannot tell how much professional attention it would have received in the absence of journalistic attention.

There is actually one advantage to trial-by-blogosphere, and that is that general understanding may progress much more quickly. Look at how many exchanges there have been between Distler and Smolin on that thread at CV, and imagine if that had to take place by exchange of preprints! It would take weeks or months.

marcus

Dec20-07, 03:44 PM

It may yet happen. But most of the blog discussion is ultimately a reaction to the mass media coverage of Lisi's original paper
...Or it might have been ignored outside of LQG. ...

You could compare this case to Joy Christian's paper, earlier in the year, claiming a counterexample to Bell's theorem. That has received about half a dozen rebuttals at the arxiv, and no blogosphere flamefest. But even that paper was in New Scientist, so one cannot tell how much professional attention it would have received in the absence of journalistic attention.

There is actually one advantage ...

I like the perspective you bring. A calm look at the whole picture.

What I get from you is a picture where even the despised popular media plays a part. Joy Christian posts on arxiv and gets plentiful rebuttals, themselves also on arxiv, partly thanks to agitation by the NewSci weekly hysteria machine.

I understand the advantage of blogs that you point out. The format itself demands rapid response. Comments quickly get covered up and lost in flurry. So quick volleys are exchanged. On the other hand there is something to be said for a slower format and more deliberate exchange. A discussionboard like PF seems to have somewhat longer-lived slower paced threads. As you observe, posting on Arxiv is even slower paced.

Sometimes it helps to say what is your Utopian vision, what you think would be ideal. What would seem ideal to me is if major figures like Smolin and Distler would confine themselves to exchange on Arxiv, in cool orderly style. And then let spectators including ourselves make noise about it. As a member of the mob of bystanders I feel confident that (with or without the help of NewSci and SciAm trombone sections) we could ensure that interesting debates on Arxiv do not go unnoticed.

Courtesy is (I hope) a separate issue. I think MORE courtesy should be required on blog and forum (than in unrecorded head-butting at the blackboard and coffeemachine). I find PF is somewhat unusual in that people actually have to be nice. Nastiness often gets deleted by the mods.

marcus

Dec21-07, 12:24 AM

I offer a clean, free-of-insults compilation/edition of what is (was) going on over at CV.

http://egregium.wordpress.com/2007/11/10/physics-needs-independent-thinkers/

Scroll down to "disclaimer".

For non-technical ramblings on the episode over at CV, see here

http://egregium.wordpress.com/2007/12/17/competitive-cycle/

and for my concerns on Lisi's theory and Distler's arguments, as well as on how far Smolin's work depends on Lisi's, see here:

http://egregium.wordpress.com/2007/12/11/garrett-and-smolin-to-boldly-go/

For technical discussions on Smolin's paper, I attempt to build a discussion here

http://egregium.wordpress.com/2007/12/07/the-plebanski-action-extended-to-a-unification-of-gravity-and-yang-mills-theory/

To which Smolin has posted a useful comment.

Thanks
Christine

Christine, You have done a remarkable editing job! I like your blog format, where you enable only those comments which meet your standards. The tone is friendly and polite.

With enablement there is a slower pace, which allows your commenters time to have a normal life, and the discussion stays on track.

Your editing the CV script down to serious technical exchange between JD and LS had a surprising effect. there is no rudeness! nobody showing off how funny they can be. I didn't realize how much actual content there was. Your edited script goes up through 19 December. I am not suggesting you continue---you know best.

I was reminded of the folk-saying: "to make a silk purse out of a sow's ear." The CV comment stream was the ear of a pig, and you made a nice scholar's dialog out of it.
the change is almost funny.

Well, I have to go wash the dishes. I hope you and Mitchell think some more about these
blog+arxiv media issues. I will. We are gradually learning by examples what does and doesn't work.

Ivan Seeking

Dec24-07, 02:06 AM

A note from Nature: Whatever happened to...
E8, that amazing mathematical structure?

E8 (or at least a 2D representation of it).American Institute of Mathematics/Peter McMullenIn March, researchers mapped a bizarre 248-dimensional object, an entity known in mathematics as E8. The map (which can be very prettily rendered in two dimensions) was touted as being useful to physicists interested in fundamental questions of quantum theory and relativity.

Then, in November, E8 surfaced again in reports of something claiming to be an exceptionally simple theory of everything, which basically involves sticking fundamental particles on various points of E8 and then looking at it in different ways to see how the particles relate to each other. The use of symmetrical structures in this way is fascinating and can be very powerful, and the story got lots of press after New Scientist highlighted it — not only because of the grand claim, but also because its source was a lone surfer with a physics degree. But physicists have since cast doubt on whether the idea is really new, really correct, or really able to make testable predictions. We’ll wait for the work to get peer reviewed for a journal, and for those crucial testable predictions to appear, before making a judgement.
http://www.nature.com/news/2007/071221/full/news.2007.390.html

ccdantas

Dec24-07, 04:46 AM

Christine, You have done a remarkable editing job!

Thanks a lot, Marcus.

The whole CV episode was a complete mess. At the end, I was sad with how things ended.

I think blogs can serve as a serious place for technical or scientific exchanges in a friendly environment, but it is not easy, really. There are much more examples showing that it doesn't work than otherwise... I had to do some off-line moderation work. You must have time, energy and a sense of neutrality. I cannot say I have all these elements, specially the first ones...

Thanks,
Christine

Coin

Dec24-07, 02:45 PM

We’ll wait for the work to get peer reviewed for a journal, and for those crucial testable predictions to appear, before making a judgement.

Incidentally, has/will Garrett's E8 proposals been submitted for peer review?

Count Iblis

Dec24-07, 07:09 PM

Incidentally, has/will Garrett's E8 proposals been submitted for peer review?

His paper has already been reviewed by many people. So, he shouldn't bother to submit it to a journal. Submitting papers to a journal is for most papers a redundant exercise as the preprint is the postprint (http://users.ecs.soton.ac.uk/harnad/Hypermail/Amsci/1011.html) anyway.

shalayka

Dec25-07, 06:55 PM

Thanks a lot, Marcus.

The whole CV episode was a complete mess. At the end, I was sad with how things ended.

I think blogs can serve as a serious place for technical or scientific exchanges in a friendly environment, but it is not easy, really. There are much more examples showing that it doesn't work than otherwise... I had to do some off-line moderation work. You must have time, energy and a sense of neutrality. I cannot say I have all these elements, specially the first ones...

Thanks,
Christine

I do agree that it was lugubrious that the conversation had to go the way it did, but it was becoming apparent that Lee Smolin had misstepped by giving unconditional praise to a paper that contained so many fundamental errors, and yet had no interest in describing what remained standing. All of this coming from someone who has such disdain for string theory as an unverified, unscientific meta-theory. The irony is ridiculous. Unfortunately for anyone who behaves in such a two-faced manner, I have a strong feeling that I'll be around for some time to come. I thought it was kind of cute that Sean Carroll doesn't realize that categorizing people as children is in itself an act of childishness. It just goes to show how high up in the clouds these peoples' heads are.

I suppose it's best said as "shut up and calculate". It's plainly obvious who's doing the talking, and who's doing the actual calculating.

Ivan Seeking

Dec26-07, 12:33 AM

His paper has already been reviewed by many people. So, he shouldn't bother to submit it to a journal. Submitting papers to a journal is for most papers a redundant exercise as the preprint is the postprint (http://users.ecs.soton.ac.uk/harnad/Hypermail/Amsci/1011.html) anyway.

The folks at Nature seem to have a different opinion.

Count Iblis

Dec26-07, 05:05 PM

The folks at Nature seem to have a different opinion.

Well, I don't see why the article would not be accepted in, say, PRD. The referees would perhaps only demand some clarifications on some contentious points. But papers are not usually rejected just because the referee doesn't agree with the author's conclusions.

Electron17

Jan15-08, 11:59 PM

If Lisi's model turns out to be correct, does that mean all of physics is essentially solved and there will be nothing left to do? Or will the details need to be worked out for many years afterward?

staf9

Jan17-08, 01:10 PM

If Lisi's model turns out to be correct, does that mean all of physics is essentially solved and there will be nothing left to do? Or will the details need to be worked out for many years afterward?

It means we have a LOT left to do, every question answered raises lots of new questions. In many ways, there may be even more that we don't know about if E8 Theory is correct. Some other people on these forums may be able to enlighten you more on this subject than I could.

ericchou

Sep10-08, 10:51 AM

Sorry! I have a question about Lisi's theory.
What different between Lisi's theory and Chaos theory?
Thank you!!

mitchell porter

Sep10-08, 08:27 PM

ericchou

Sep11-08, 12:31 PM

Lisi's theory is a theory about what the fundamental particles are and how they interact.

Chaos theory is about a type of unpredictability which happens because small uncertainties are amplified into large uncertainties. Such "chaos" is a very general phenomenon and happens everywhere there are even moderately complicated interactions. You should look it up on Wikipedia to understand it better.

Sorry!! If Lisi's theory is correct, then chaos & lisi's theory must be some relations between them.

and Do you believe the fate? I see something in the future, and it relate with chaos.

mitchell porter

Sep11-08, 09:17 PM

Like I said, chaos is a very general phenomenon. Every physics theory since Newton's gravity allows chaos. Read the Wikipedia article.

Xezlec

Sep14-08, 04:11 PM

I understand precisely 0% of this subject.

However, at http://golem.ph.utexas.edu/~distler/blog/archives/001505.html where Jacques Distler blasts the theory in an extremely rude and inappropriate way, demonstrating an inability to interact like a human being and making physics look like an ugly, ugly little world in the process, he sure does appear to win the heck out of whatever argument he's having, at least to my uncomprehending eyes.

Am I correct to understand that Distler claims to have mathematically proven that E8 theory is inconsistent with the existence of third-generation fermions?

I also noticed that G. L. responds and gets into a one-sidedly civil conversation in which he appears to admit that:

1. Distler is right, though Lisi thinks there's still something useful about his theory, and
2. Distler has correctly pointed out another error in his reasoning (see the "WHILE YOU'RE HERE" thread in the comments).

Is my understanding correct?

Ivan Seeking

Dec31-08, 08:33 PM

In the news:

Did Garrett Lisi Have a Wipeout?
...Perhaps the longest public debate on the merits of Lisi’s theory took place primarily between Jacques Distler of the University of Texas at Austin and Lee Smolin of the Perimeter Institute for Theoretical Physics in Ontario, the latter of whom had been widely quoted in the media with unqualified praise for the theory. (Smolin says he was quoted out of context.) Smolin had also quickly written a paper suggesting ways to correct certain flaws in the E8 proposal. For the particles in the E8 theory to represent the known particles properly, the combination of smaller groups used to form the Standard Model must be embedded inside E8 in just the right way. Distler had demonstrated in his blog that this is a mathematical impossibility. So far as he was concerned, the theory was dead and not worth trying to resuscitate. Yet argument raged on over details of Distler’s proof and ultimately ended with neither side conceding. Lisi, incidentally, played very little part in these disputes.

Today the theory is being largely but not entirely ignored. Lisi, naturally, continues to work on it, as does Smolin. Lisi says that even if what Distler claims is true, it would only be true for the variant of E8 (“real E8”) originally used in his paper and that another variant (“complex E8”) would certainly work. Smolin argues that the press coverage gave the false impression that Lisi’s proposal was a finished work. “In reality,” he says, “almost every new theoretical proposal is first presented in a way that is flawed and incomplete, with open issues that need to be filled in.... While Lisi’s proposal has exciting aspects, this is the case with it as well.”
http://www.sciam.com/article.cfm?id=garrett-lisi-e8-theory