An Exceptionally Simple Theory of Everything!

**marcus** · Nov6-07, 08:11 PM

http://arxiv.org/abs/0711.0770
An Exceptionally Simple Theory of Everything
A. Garrett Lisi
31 pages, 7 figures
(Submitted on 6 Nov 2007)

"All fields of the standard model and gravity are unified as an E8 principal bundle connection. A non-compact real form of the E8 Lie algebra has G2 and F4 subalgebras which break down to strong su(3), electroweak su(2) x u(1), gravitational so(3,1), the frame-Higgs, and three generations of fermions related by triality. The interactions and dynamics of these 1-form and Grassmann valued parts of an E8 superconnection are described by the curvature and action over a four dimensional base manifold."

This paper is visually a treat.

Too bad i can't print it out in color.

=========UPDATE==============
In post #7 here, Christine tells us that Bee has a discussion of quantum E8 theory at her blog:
http://backreaction.blogspot.com/200...eption-of.html

**starkind** · Nov6-07, 09:16 PM

Thanks, Marcus. I was hoping to find a link to this paper. Congrats, Garrett

**marcus** · Nov6-07, 10:41 PM

first, it is in part understandable.
many people here at PF could read it and get something out of it

second, I get a funny feeling in my gut reading it----it hits me that it could be right.

but most importantly, I gather, it is predictive. there are no free parameters to fudge around. you can unambiguously derive testable quantities. so it is unambiguously right or wrong---clear and forthright either way.

So I am curious to know, is numerical computation at all applicable? And if so, what kind of computing power would it take to derive some new predictions from this ToE?
Dan Christensen at University of Western Ontario has shown an interest in using the supercomputer there to calculate stuff from QG models---spinfoam and other.

what kind of thing might one be able to predict, either by numerical or analytical means, or both, from the ToE?

**garrett** · Nov6-07, 11:31 PM

In Morelia I asked Dan Christensen what he thought about the prospect of calculating 10j symbols for an E8 spin network, and he said he found it terrifying. Rightfully so.

This theory is either very right or very wrong -- it could go either way. There are still a few things I don't understand about it, so it's premature to make predications with any confidence yet. But the predictions will come, and make it or break it. It aint over 'till the LHC sings.

**jal** · Nov7-07, 09:34 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:+Q.../0/1/0/all/0/1 and the work done by Tony Smith http://www.valdostamuseum.org/hamsmi...wsbadnews.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, 09:35 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, 10:29 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, 10:40 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, 11:09 AM

Originally Posted by marcus

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, 11:14 AM

Originally Posted by jal

I am remembering the work done by Chris Quigg and The Double Simplex http://arxiv.org/find/hep-ph/1/au:+Q.../0/1/0/all/0/1 and the work done by Tony Smith http://www.valdostamuseum.org/hamsmi...wsbadnews.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, 11:22 AM

Originally Posted by ccdantas

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, 12:53 PM

Here's the link to Bee's discussion
http://backreaction.blogspot.com/200...eption-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/200...64169156800942

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, 02:13 PM

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

**garrett** · Nov7-07, 03:01 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, 05:00 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, 05:01 PM

Hi, Garrett.

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

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

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:

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

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/showthr...98#post1496398

Regards, Hans