An Exceptionally Simple Theory of Everything

[arivero]

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

 

[Coin]

Hi,

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

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

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

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

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

 

[jal]

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

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

and at the link from Mephisto

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

 

[staf9]

Congratulations Garrett!

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

In addition:

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

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

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

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

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

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

 

[CarlB]

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

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

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

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

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

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

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

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

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

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

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

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

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


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

 

[marcus]

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]

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.)

 

[CarlB]

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]

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]

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]

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]

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]

strangerep, thanks for the clarification.

 

[Nereid]

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 http://www.arxiv.org/abs/math.DG/0612069" ' on Garrett?

 

[CarlB]

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]

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

Nice applet Carl, has real promises to become a good tool to study the E8 rootsystem.

Regards, Hans

 

[shoehorn]

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]

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.

 

[datakleptomanic]

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

 

[check]

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]

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]

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]

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]

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]

...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 )
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]

that's exciting. do you happen to know where? connected with what institution?
(never mind that's just how my mind works )
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]

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]

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]

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]

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

 

[Fredrik]

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]

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]

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 ). 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 and this page (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:

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]

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]

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]

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]

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]

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]

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]

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]

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/babe...-0@2-3244,36-979858@51-979860,0.html&lp=fr_en

 

[chrisina]

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 definately 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]

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. isn't 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]

thx Marcus, what about the number of free parameters ?

 

[Coin]

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 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...

 

[member 11137]

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]

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


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.

Indeed, many new particles are predicted and I really hope that these particels will indeed be found. What is disturbing though is that gravity also seems to be mediated by virtual particles. So, gravity is treated as an ordinary force whereas there are a number of indications that point in a different direction. Therefore, I think that this is a "theory of everything" - except for gravitation.

Rudi Van Nieuwenhove

 

[marcus]

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]

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]

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