An Exceptionally Simple Theory of Everything

[CarlB]

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

 

[jal]

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

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

 

[garrett]

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

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

 

[CarlB]

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

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

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

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

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

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

 

[marcus]

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

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

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

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

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

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

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

 

[Mephisto]

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

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

 

[christianjb]

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

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

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

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

 

[Ivan Seeking]

This is all very exciting!

Congratulations Garrett, and good luck!

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

 

[marcus]

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

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

 

[arivero]

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

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

 

[arivero]

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

 

[Coin]

Hi,

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

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

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

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

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

 

[jal]

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

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

and at the link from Mephisto

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

 

[staf9]

Congratulations Garrett!

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

In addition:

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

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

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

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

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

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

 

[CarlB]

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

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

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

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

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

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

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

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

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

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

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

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

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


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

 

[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.