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An Exceptionally Simple Theory of Everything


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This paper by Garrett Lisi, http://arxiv.org/abs/0711.0770, is raising quite a stir in the physics world.



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.


Some physics blogs that discuss this paper:




The 248 dimension exceptional Lie algebra E8 is discussed here



Lisi does not require any extra dimensions than the three spatial dimensions and time we already know about. In fact, detection of extra spatial dimensions by the LHC might well falsify Lisi's theory. Lisi also predicts 18 new particles, another test. Finally, the theory has no free parameters (aka fudge factors).

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I've not read the paper; neither am I completely sure what the purpose of this thread is. Anyways, to get some discussion started:


What is a "free" parameter? Isn't it a parameter that is not fixed by the theory itself but must be measured experimentally? Examples: The speed of light, the mass of an electron, the QED coupling strength. As an alternative question (for the case we roughly agree on the understanding of the term "free parameter"): How does this approach manage to reproduce Standard Model physics without free parameters, particularly in the light of the non-gauge interactions (with non-gauge interactions having arbitrary coupling constants almost by definition) required for the electroweak symmetry breaking? Does this model reproduce the SM at all?


A more general question (not to be mistaken as being pejorative): Why should anyone bother reading this paper and who would this "anyone" be?

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I bet the day it gets "discovered" what the (next) connection (we find) is, it will probably be some grad. who says to his prof. "But hang on, when I do this...?!". But maybe it will be at some collider or gravitational wave observatory, or whatever (I bet that's what all the teams there are hoping, anyway).

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A more general question (not to be mistaken as being pejorative): Why should anyone bother reading this paper and who would this "anyone" be?


You might want to read this paper because, if it is right, it might well signal the end of string theory. The author has a PhD in physics from UCSD. The two blogs are by Peter Woit, a professor of mathematics at Columbia University, and Sabine Hossenfelder, a theoretical physicist at the Perimeter Institute for Theoretical Physics. In other words, neither slouches nor quacks.


The paper is daunting, which is why I added John Baez' writeup on the exceptional Lie algebras.

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DH, thanks for posting this. It is an excellent find.

also thanks to Riogho for spotting it and posting in General Physics ( http://www.scienceforums.net/forum/showthread.php?p=370366#post370366 )


At Sabine's blog the discussion started 6 November and is still very lively after 5 days. They have just been joined by Fabrizio Nesti (SISSA-Trieste)

Here is Nesti's first post, scroll down to find subsequent ones.



Here are some of Nesti's papers



I find it interesting that he has co-authored recently with Roberto Percacci, who is also at SISSA-Trieste.

Percacci is important in my view certainly in quantum gravity but he also works in particle physics (where others would be a better judge). Here is the recent Percacci-Nesti paper, which I dont think is in the Spires list above.





I guess it is well known that Lisi is the recipient of a grant from the FQXi. this is a new private foundation that so far AFAICS has been considerably smarter than the Macarthur in picking recipients of their grants. Macarthur Foundation is the one with the famed "genius awards". In Lisi's case I would say that FQXi is definitely getting their money's worth.

FQXi is chaired by Max Tegmark (MIT) one of the co-discoverers in 1998 of ("dark energy") the positive cosmological constant.

Frank Wilczek (Nobel, MIT) and Lee Smolin (Perimeter) are on his advisory board. It is a classy outfit.




there is this very sensible question "who should read this paper?"

and I guess the simplest answer would be anyone who wants to follow what is going on with Quantum Gravity and Unification and they should scan it to find parts they can understand, and get an idea from other people as best they can

(because quite a lot requires extensive knowledge of Lie Groups and their representations, and the differential geometry of bundles and connections, so it isnt easy reading!)


the paper is in some sense "where it's at" right now and one should get from it at whatever depth one can.


DH mentioned that it is about E8 the largest of the eight exceptional Lie Groups, and the lowercase e8 stands for the corresponding Lie Algebra. this has dimension 248.

Eight of these are for the "Cartan subalgebra", a commutative kernel which provides a framework for calculating the structure of the rest, so not included in it. The rest has dimension 240, and these dimensions get assigned to PARTICLES.

The rest, excluding the small 8D kernel, has a structure schematic diagram called a root diagram. Essentially the structure is given by a basis of 240 eigenvectors and an 8D space of eigenvalues of the Cartan subalgebra action.


How the 240 basis vectors interact (via the Lie bracket multiplication one with the other) mimics how particles interact.


222 basis vectors for 222 of the dimensions are assigned to KNOWN particles---they take care of all the generations and colors of the standard model particles.


Then there are 18 dimensions more, so 18 basis elements, which are assigned to CONJECTURED particles.

There may not be 18 separate ones, there may be fewer and just coming in different flavors or colors or whatever

and that comes to 222+18 = 240.


The dimension of the "Cartan subalgebra" is called the RANK of the Lie algebra. And the exceptional group E8 is called E8 because it has rank = 8. The Cartan subalgebra seems to be the key to unlocking the structure of the Lie Algebra, tantamount ot understanding the group itself. What defines it is being the largest bunch of elements that commute with each other---have null commutator bracket with each other.

OK so this is a bit technical. for more information look at


or maybe even better just look at page 4 of Garrett's paper which has a clear simple explanation


everybody with a fast enough connection should watch this beautiful movie of the E8 root diagram



if Lisi is right, the root diagram schematic of this group E8 is the "periodic table" of matter+geometry

Remember that the root diagram of the E8 group schematizes the group and shows how the basis elements interact----in the particle case, what particles can interact with what other particles to make what. This root diagram schematic exists in 8-dimensional space and the movie is of a projection of it onto your computer screen, as it ROTATES. Seeing the 8-dimensional periodic table of matter+geometry rotating and projected, gives a better idea of its layout than just one still shot would do.


and Lisi could certainly be WRONG, which a scientific theory should be testable and falsifiable by its predictions, and he and others will be busy deriving a lot of predictions to be tested----either way, win or lose, it is good science. great, I think.


Garrett Lisi is giving a talk (at the International LQG Seminar) today. His slides are available online at the ILQGS site, and the audio will presumably be posted later.


Assuming the hook-up is successful and the seminar comes off as usual, there will be comment and questions from major Quantum Gravity people. It will be interesting to see how Lisi gets along with them.


The seminar is in progress at the moment. Here is the website where the PDF of the slides is posted



they start the seminars at 7AM pacific which I guess is 3PM GMT so that it will not be too late for people in other places (Berlin, Marseille..) to participate.

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Thanks much, Martin. I have much to learn to be able to grasp the concepts laid out in this paper. I posted the link to this paper because this paper, if it is right, may be truly groundbreaking.

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I skimmed this paper the other day and saw enough in it that I recognised to make me want to sit down and study it properly. I also picked up some very negative comments. But even if this paper is flawed, as I speak I think it's pointing in the right direction.

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But he also doesn't attempt to fix the fact that gravity is not renormalizale.

You seem not to know what you are talking about, Ben, because your statement suggests that it is a "fact" that gravity is not renormalizable.


This has not been proven, and indeed there is considerable weight of evidence to the contrary: namely that gravity IS renormalizable (along nonperturbative lines Steven Weinberg laid out in 1979). A number of people have been working on this lately. Garrett Lisi cited these people's work today in a seminar talk---slides and audio are online.


I am not saying the evidence for renormalizability is conclusive as yet, merely that your statement is groundless.


If you think you can back up what you said, please give us some links to online evidence that we can all look at. Of course I mean renormalizable outside the perturbation series context. The perturbative case is uninteresting because gravity has been known for a long time to be not renormalizable in that case.

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I read the paper with interest, lingering on phrases like "there is a classic principle for restricting the possibilities" and automatically wanting to unflatten the cube on page 5 and spin it on a vertex looking for my trefoil. I couldn't help thinking in terms of a cube of space with xyz axes, where degrees of freedom are extension in different directions, eg:


1. x

2. y

3. z

4. xy

5. xz

6. yz

7. xyz

8. none


..but I left the paper at home along with my notes, and there's a lot I need to look up, so I'm currently scratching my head at "classic" and "how the E8 manifold twists and turns over spacetime, reproducing all known fields and dynamics through pure geometry".



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You might want to read this paper because, if it is right, it might well signal the end of string theory.The author has a PhD in physics from UCSD. The two blogs are by Peter Woit, a professor of mathematics at Columbia University, and Sabine Hossenfelder, a theoretical physicist at the Perimeter Institute for Theoretical Physics. In other words, neither slouches nor quacks.

My question was meant a bit more specifically than "the author is not the typical sfn crackpot". And while "the author is no crackpot" probably is a necessary criterion to get interested in a paper, it certainly (not last due to the issue of limited time per day) is not a sufficient one to bother reading a paper. hep-ph alone has probably something like 5-10 papers/day, and I surely do not read them all.

Just looking at the very first current entry in new, I read "TeV gravity in four dimensions?". From the topic, I see that the model might be in collider range, i.e. principially testable in collider experiments and that the model claims not to need extra dimensions. From the end of the paper (I've really only read the title and the very last sentences, I don't know the names of the authors, either) it seems that there is some rough approximation of a cross-section for whatever process. That further indicates that their idea might be testable. So if I was interested in quantum gravity or currently working on related stuff, I might go one further step and actually skim the paper because "no extra dimensions" and "possibly testable predictions" looks interesting.


Ok, I hope I have roughly described what I mean by "why someone should read something". How does this fit to the paper you proposed? What is new compared to other approaches? Are there any predictions? Is the paper supposed for people with other criteria than me? In that case, who would that be (except for Martin :D) and what would these criteria be (also in the case of Martin)?

EDIT: Perhaps the answer is simply that the paper is not interesting for me because I am not working in quantum gravity but you probably wouldn't expect anyone working in that field to learn of it from an sfn thread if it really was an important contribution to the field.

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Just looking at the very first current entry in new, I read "TeV gravity in four dimensions?". ...


You picked a good example! I saw that paper yesterday. You say you don't know the authors, I don't know the first one either. But I have read several papers by Steve Hsu and even started a thread here at SFN about one of them in particular. He is a smart guy and has an interesting blog called "informationprocessing"

Teaches at Oregon State if I remember. Co-authors a lot with Anthony Zee.

They posted an interesting approach to resolving the blackhole information paradox within the past year.


I agree that the abstract makes this one sound interesting because promises not to require extra dimensions and also to make falsifiable predictions (distinguishes it from usual string philosophy)


Maybe we should have a thread just putting links to interesting finds. You could post this one.



TeV gravity in four dimensions?

Xavier Calmet, Stephen D. H. Hsu

5 pages

(Submitted on 14 Nov 2007)


"We describe a model in which the fundamental scale M* of the theory which unifies gravity and quantum mechanics is in the TeV range, but without requiring additional spacetime dimensions. The weakness of gravity at low energies is due to a large vacuum expectation of a dilaton like field. The model requires a small dimensionless parameter (the self-coupling of the dilaton) but no fine-tuning. We discuss in detail the dynamical assumptions about nonperturbative quantum gravity required within the model. We observe that M* could be quite small, less than a TeV, and that the model could lead to copious strong coupling effects at the LHC. However, semiclassical black holes will not be produced."


It's D H's thread. Maybe he would be happy if the thread evolved into a "interesting recent postings on arxiv" thread. If D H likes this, I think it would be great. If he doesn't like it and wants the thread to stay focused on Garrett Lisi's paper, that's fine too. We can start a recent-finds-on-arxiv thread some other time.

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It's D H's thread. Maybe he would be happy if the thread evolved into a "interesting recent postings on arxiv" thread. If D H likes this, I think it would be great. If he doesn't like it and wants the thread to stay focused on Garrett Lisi's paper, that's fine too. We can start a recent-finds-on-arxiv thread some other time.


If you want to do that, the most interesting paper in Friday's list is

arXiv:0711.2473, Parton Distributions for LO Generators, A. Sherstnev, R.S. Thorne


But maybe I am just boring...

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If you want to do that, the most interesting paper in Friday's list is

arXiv:0711.2473, Parton Distributions for LO Generators, A. Sherstnev, R.S. Thorne


I think it would be great if people would throw into a common pot what new papers they find most interesting. This thread could work that way if D H wants. It already has kind of a cute title for such a thread and it is already started. So I would think serendipitous if DH says OK and we just keep going!


How about that DH? Your call, either way is fine.

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It's D H's thread. Maybe he would be happy if the thread evolved into a "interesting recent postings on arxiv" thread. If D H likes this, I think it would be great. If he doesn't like it and wants the thread to stay focused on Garrett Lisi's paper, that's fine too. We can start a recent-finds-on-arxiv thread some other time.


I think a recent-finds-on-arxiv thread is a great one. My only objection to making this thread the "recent-finds-on-arxiv thread" is the title of the thread itself. I can no longer change the title. If a moderator can change the title, go for it. Approval granted.


OTOH, if no one can change the thread title (or if the powers-that-be don't like the idea), I think it would better serve the forum to keep this thread to the original topic of Lisi's paper.

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OTOH, if no one can change the thread title (or if the powers-that-be don't like the idea), I think it would better serve the forum to keep this thread to the original topic of Lisi's paper.


I don't qualify as "powers-that-be" but I like the idea of starting a new thread for recent finds, and keeping this thread for discussing the Garrett Lisi paper, titled as it is.


I hope that's what we do.


If anyone reads French, there is a nice short article about the reaction to Lisi's paper in LE MONDE, today.


I will get the link.




down at the bottom there is a "print this article" button that gets a printer-friendly version




So getting back to discussing this specific paper, its impact and the discussion it stirred up....


I'll start making a rough translation of the article in Le Monde and anyone who knows French and wants to help please do. Take over any part of the job.


I will start partway thru the first section. The headline and the first part would be more difficult to get right because they are idiomatic.


======exerpt translated from Le Monde 19 November======


...To do this, explains Carlo Rovelli of the Center for Theoretical Physics at Marseille, "we are confronted by two problems". "The first is to describe, using the same set of equations, all four fundamental forces of nature: the strong interaction, the weak interaction, the electromagnetic force, and the gravitational force," the researcher explains. "The second is to make the two theories, quantum mechanics and general relativity, compatible."


We have to check the calculations


"Up to now, string theory [a grand unification theory developed at the end of the last century] has solved the first of these problems well, but the second rather poorly," adds Carlo Rovelli. "As to the theory of Loop Quantum Gravity, which I work on, it solves the second problem but says nothing about the first. The theory of Mr. Lisi looks like it might be able to solve both problems at the same time, with a very beautiful mathematical formalism."


Can a snowboarder have succeeded where hundreds of researchers trained at the greatest institutions have failed? It is very far from being a certainty, but the possibility is not a matter of indifference. A teleconference on the subject, involving some fifteen research groups, triggered, according to Rovelli, "much exchange of email." ...




I will translate some more as time permits.




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Peter Woit of Not Even Wrong (in)fame(y) had a mixed albeit slightly optimistic review:




Most of the negative reviews of this I've seen have been in the form of ad hominem character assassination (calling him "surfer dude"), although I've seen the inclusion of a number of scientific complaints regarding the mixing of incompatible parameters. Sadly, I don't have links offhand.

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Here's a picture of it:





"On paper, the calculation would cover an area the size of Manhattan. But an international group of 18 mathematicians and computer scientists, including two from MIT, has found a more practical way to calculate the inner workings of E8, one of the most complicated symmetrical structures in mathematics. Mathematics professor David Vogan and Dan Ciubotaru, an instructor in the math department, were among those who put the supercomputer Sage through a 77-hour computation to calculate the 200 billion numbers in E8's character table, generating a 60-gigabyte file.


E8 is an example of a Lie group--a continuous symmetry group whose structure is always transforming yet, like a sphere rotating around an axis, always looks the same. All but five Lie groups fall into one of four classes related to linear algebra and Euclidean geometry. E8 is the most complex of these five "exceptional" Lie groups. It describes the symmetries of a 57-dimensional object that can be rotated in 248 ways without changing its appearance. Calculating its character table--a 453,060-by-453,060 matrix that describes all the ways E8 can appear as a symmetry group--is just one important step toward understanding all Lie groups, says Vogan.


This computer-generated illustration is of the E8 root system, an arrangement of 240 vectors in an eight-dimensional space. The image is a two-dimensional projection of that eight-dimensional arrangement."

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I just realized there are two pieces in Le Monde: the article and an interview.


The main article, and printerfriendly version:




Fish translation of the article




The interview, in printerfriendly version:



Fish translation of the interview:



==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 only one and even theory. This 39 year old American, until now unknown, is attached to no university, any laboratory. Its work is not less, since the beginning of November, in the sharp discussions center 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 to earn as little my living, as possible, dedicating the majority of my time to the equations and benefitting from the full air.


Then, one year ago, I postulated for obtaining a purse near a 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.



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An Exceptionally Simple Theory of Everything


I am just a layman and what I can read on it is that it is anything but simple...

What I can understand from that is only that this 'mathematical structure' (E8) describe well the world. Remind me a little bit of the epicicle:

It doesn't fit ? And more dimension...

Do I need to know QM to appreciate the simplicity ?

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Jacques if you know what "in-joke" means, I would really like to know the French idiom for "inside joke".


Math and physics people always have these jokes and puns (double entendre?) that refer to the technical terminology of their specialites.


In the mathematics of Group Theory there is the technical concept of a simple group.


As it happens, E8 is a simple group. (it doesnt have to do with ordinary ideas of simplicity)


also E8 belongs to a small number of groups called the EXCEPTIONAL LIE GROUPS. It is the largest exceptional Lie group.


All the exceptional Lie groups are simple.


The moment I saw the title of Garrett's paper I started laughing because he had made a witty play on words----with some mockery or mild irony also.


It is not yet a complete Theory of Everything either, this term "ToE" has always been a gross exageration used by string theorizers. One of the extravagant promises that has never been fulfilled in over 20 years. So for Garrett to use "ToE" in his title was also a kind of subtle mockery.


He is a complex person. I took the title of the paper to be more witty than serious. But everyone can see it as they wish, there is certainly no one correct view.



in case anyone is curious, a simple group G is intuitively one which cannot be collapsed down to a smaller group H


there is no non-trivial many-to-one mapping that preserves multiplication

that is, no group-mapping phi that goes G --> H, unless either it is one-to-one or H is the group with one element.

if you know Bourbakistic terms like surjection and injection then any nontrivial surjective homomorphism must be injective

and the same can be expressed in terms of subgroups----the non-existence of a certain type of subgroup of G.


the intuitive idea is that a simple group G has been collapsed down as far as it possibly can be collapse. all the air and water have been squeezed out and it is down to hard essential structure


but this does not make it simple in ordinary layman's language, only perhaps it is MORE simple than it MIGHT have been.

but still can be quite intricate!

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I saw a rather critical review of this paper, which unfortunately I cannot find anymore.


The critic cited descriptions in the paper which expressed sums of certain forces which the critic considered incompatible.


Have you seen anything along those lines?

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Hi Bascule,

Sorry for not responding earlier. Holiday intervened and I didn't see your post until now.


G.L.'s first shot at a ToE does have serious flaws and he has been pretty frank about pointing out where he thinks it needs more work


I think the main question to be asking is whether or not there are some new ideas here that can be put to use.


There is a big discontinuity between the splash his paper made in the media (because interviewing Garrett makes good copy---for one thing he has a good sense of humor, plus of course the atypical lifestyle)

and the actual situation within the nonstring QG community.


Of course the stringfolks damned him fervently up and down non-stop. He infringed on their image.


But that doesnt matter. The real reason Garrett came out with his paper at this point----which he was thoroughly up front about----was it was time to get more people working on it.


He had made a good enough beginning that he thought he could recruit collaborators, and other people to help by working independently along similar lines. And there is a great deal of work to be done.


Not only does he have bugs to work out---but his entire theory (even assuming he gets all the glitches smoothed out---is not yet a quantum theory. What he has is a superstructure which it MIGHT be possible to graft onto LQG.


LQG is a quantum theory of geometry where the geometry is represented by a math object called a CONNECTION. Einstein described geometry with a distancefunction called a METRIC and later, at least by 1980s, people found out that you could drop the metric and use a connection instead.


Intuitively a connection is something that describes how structures twist and roll as you slide them about on the hypersurface---so it relates the tangentvectors at one point with the tangentvectors at a neighbor point. A connection lets you do parallel transport---it gives a meaning to that.


All this so far is CLASSICAL. What LQG did in the 1990s was formulate a quantum theory of connections, so you could have a hilbertspace of quantum states of the geometry of your continuum.


But the kind of connection that LQG deals with is quite rudimentary and only encompasses geometry (that was the original idea)


What Garrett offers is a much larger fancier type of connection that encompasses matter and forces. But it is not yet QUANTIZED.

(and it has other bugs which hopefully can be worked out, but that is the main lack that I see)


What he has basically done is apealed for LQG people to team up with him. This came out in the ILQGS (a conferencecall seminar called international LQG seminar) that was held soon after the appearance of his paper.


in a sense it is make or break now. It's a big job and he can't do it all. Either other people from nonstring QG community will join in, and his theory will mature and make some progress (whether ultimately right or wrong doesnt matter yet, tests are in the future) or it will not attract collaborators and it will fade from sight.


there have been some positive responses, but we won't know until we start seeing papers by new authors or by Garrett and others.


that's a quick assessment, may be quite wrong but that's my take at the moment.


have to go.

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I read a critic (I'll now be compelled to find this again -and I have to apologise pre-emptively because my pc is mid-mobo upgrade and I have 3 different 64-bit brand new linux (linuces?) I'm giving a tryout -phew): said that Lisi is mistakenly associating a non-transitive (or associative) group with a F8 sub-group that isn't. So he's whistling in the wrong key, according to this dude (I think I might have followed a link from a news feed).


Found it:http://motls.blogspot.com/2007/11/exceptionally-simple-theory-of.html


If you care how the forces and particles are supposed to be embedded into his group, it's like this. You start with a non-compact real form of E8. You embed a G2 into it. Its centralizer is a non-compact version of F4. Now, you embed the strong SU(3) into the G2 while the non-compact F4 acts as the source of a "graviweak" SO(7,1) group that contains SO(3,1), a "gauge group" that is now fashionable in the circles of amateur physicists to "describe" gravity, and SO(4), their source of cargo cult electroweak symmetry.


Of course, the SO(3,1) group mentioned a minute ago plays a different role (in the vielbein formulation of general relativity) than the Yang-Mills groups and the fact that these two kinds of a group cannot be merged is the content of the Coleman-Mandula theorem to be discussed at the end of my text. Moreover, the fermions clearly can't arise from the connection because they have a different spin and statistics and they don't transform in the adjoint representation. For people like A. Garrett Lisi, it is not hard to unify everything with everything else because they don't know any difference between different concepts in physics.

--Luboš Motl


P.S. Some (I won't say who) are rumbling away about various aspects of recognition and are waiting for Lisi's book...


Can someone explain to me what E8 is?


Try to picture a spherically inverted multifaceted poly-dimensional plexoid of random size, add in an elemental variable thermal/mass coefficient linking system based on the gravitational and magnetic field enhanced rate of change fluctuations of sub-atomic particles and it all comes together like butter and honey on toast. Well, butter and honey don't really come together on toast but you get the idea...

--ROMRIX slashdot.org
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