An Exceptionally Technical Discussion of AESToE

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In summary, This thread is discussing technical questions from researchers and students regarding a paper on the unusual math and notation used in vector-form contraction. The thread is meant to be quick and conversational, with the main purpose of elucidating these mathematical tools and tricks. Participants can use TeX to typeset equations, but non-math related discussions are not appropriate. The paper has been peer reviewed and errata have been identified and will be corrected in a revision. The g2-su(3) relation and how it is defined and combined is being discussed, with an explicit example shown in eq(2.3) on p6. The Lie algebra and representation spaces are being treated as vector spaces, with the "+" representing a direct sum. The
  • #281
While it has always been my argument that many aspect of the lessons we learn out of condensed matter physics can be fundamental and applicable to a wide range of physics field, I also think that it needs to be applied or referred to accurately.

Lawrence B. Crowell said:
The symmetry of the lattice determines the spectra of phonons in much the same way that a symmetry group in particle physics determines the structure or states of elementary particles. The particle states are given by eigenstates of Bloch waves on a lattice, which in lattice QCD are analogously seen in Mantin periodic Lagrangians.

This is not quite correct. While the symmetry of the crystal structure can certainly be a factor in determining the phonon spectrum, it isn't the the only one, and it isn't uniquely determined by it. The form factor of the crystal structure is also one crucial aspect. That's why you can have 2 bcc lattices with the same lattice atoms, but you can easily have different basis at each of the lattice points and thus, different form factors, which in turn changes the phonon spectrum.

If small spheres are assigned to these points the lattice is a body centered cubic lattice (bcc), where the bcc in three dimensions is the crystalline lattice of silicon.

I'm sure this isn't a crucial mistake. , Still, since you are mentioning the "crystal structure" rather than the reciprocal lattice structure, silicon is an FCC diamond crystal, not bcc.

In this way the mass of the gauge particle (analogous to a massive phonon) is renormalized in much the same way massive particles have renormalized masses in a Brillouin zones.

A "massive phonon" is a rather strange term. In the heavy fermion system, there are no "massive phonons". Rather, the renormalization is due to several many-body interactions, possibly even the spin-fluctuation interactions. This is certainly confirmed by the fact that there are many systems that share the same crystal structure as the heavy fermion system. Yet, those other systems do not have the same heavy fermions. So if what you mentioned earlier that the phonon spectrum is only dependent on the crystal lattice, this observation would be inconsistent to that claim.

Zz.
 
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  • #282
ZapperZ said:
This is not quite correct. While the symmetry of the crystal structure can certainly be a factor in determining the phonon spectrum, it isn't the the only one, and it isn't uniquely determined by it.

I'm sure this isn't a crucial mistake. , Still, since you are mentioning the "crystal structure" rather than the reciprocal lattice structure, silicon is an FCC diamond crystal, not bcc.


A "massive phonon" is a rather strange term. In the heavy fermion system, there are no "massive phonons". Rather, the renormalization is due to several many-body interactions, possibly even the spin-fluctuation interactions. This is certainly confirmed by the fact that there are many systems that share the same crystal structure as the heavy fermion system. Yet, those other systems do not have the same heavy fermions. So if what you mentioned earlier that the phonon spectrum is only dependent on the crystal lattice, this observation would be inconsistent to that claim.

Zz.

The role of fermions complicates this picture, and this is something which of course is of interest to me. Solid state physics has a lot of dependencies with the electronic structure of the atoms in a lattice. Here the analogue is "weak," for the Fermionic sector is not determined in the same manner. Also I calculated a "k" for a YM field with a renormalized mass, which implicitely is a reciprocal lattice calculation. The idea here is motivated by solid state physics, but is not identical to it.

The massive phonon comparison is made since this calculation is for the mass of a QCD-like or gluon-like particle. How the fermion sector comes into play is a "work in progress." So what I presented was the basic core idea, and that interaction Lagrangian I left untouched is an area to explore. Heavy fermionic systems, such as the breakdown of Landau electron liquids, is something which I think has analogues with the vacuum structure of the universe. The quantum critical point I suspect is a point where we identify the equation of state for the vacuum with w = -1. In the toy calculation I did I simply demonstrated a way of arriving at a "tower" of masses, here given by an unspecified YM field.

Lawrence B. Crowell
 
  • #283
Lawrence B. Crowell said:
The role of fermions complicates this picture, and this is something which of course is of interest to me. Solid state physics has a lot of dependencies with the electronic structure of the atoms in a lattice. Here the analogue is "weak," for the Fermionic sector is not determined in the same manner. Also I calculated a "k" for a YM field with a renormalized mass, which implicitely is a reciprocal lattice calculation. The idea here is motivated by solid state physics, but is not identical to it.

The massive phonon comparison is made since this calculation is for the mass of a QCD-like or gluon-like particle. How the fermion sector comes into play is a "work in progress." So what I presented was the basic core idea, and that interaction Lagrangian I left untouched is an area to explore. Heavy fermionic systems, such as the breakdown of Landau electron liquids, is something which I think has analogues with the vacuum structure of the universe. The quantum critical point I suspect is a point where we identify the equation of state for the vacuum with w = -1. In the toy calculation I did I simply demonstrated a way of arriving at a "tower" of masses, here given by an unspecified YM field.

Lawrence B. Crowell

I'm not arguing about the "motivation, but not identical" part. I'm arguing that when you invoke principles from solid state physics, you are using them in error, or citing "non-existent" concept, such as "massive phonons". The existence of a "renomalized" or "effective" mass in condensed matter can be due to a number of factors. In fact, at T close to zero, there are no phonon-active effects, yet you still have mass renormalization. So this clearly indicates that this isn't a "phonon" effect, or at the very least, it isn't a major contributor to the mass.

You can do whatever you like, but it would be in error to make an analogy to something that doesn't exist.

Zz.
 
  • #284
ZapperZ said:
I'm not arguing about the "motivation, but not identical" part. I'm arguing that when you invoke principles from solid state physics, you are using them in error, or citing "non-existent" concept, such as "massive phonons".
Zz.

Ok fair enough. Clearly there are no massive phonons in Ashcroft & Mermin solid state physics. Yet one could do a "what if" and imagine a massive phonons, or in my case phonons which come about from a compactification.

Half of physical ideas come from "what if."

Lawrence B. Crowell
 
  • #285
Lawrence B. Crowell said:
Ok fair enough. Clearly there are no massive phonons in Ashcroft & Mermin solid state physics. Yet one could do a "what if" and imagine a massive phonons, or in my case phonons which come about from a compactification.

Half of physical ideas come from "what if."

Lawrence B. Crowell

Then you shouldn't cite from "solid state physics" when it doesn't come from solid state physics. Secondly, this becomes be highly speculative, which, as you are aware of, belongs in the IR forum, even for something in this sub-forum.

Zz.
 
  • #286
ZapperZ said:
Secondly, this becomes be highly speculative, which, as you are aware of, belongs in the IR forum...

ZapperZ, there are clearly many of us working on similar ideas for QG, so banning it from this forum would be roughly the same as banning strings or LQG, which is to say, just ridiculous. Moreover, the mass matrices do in fact offer some evidence that these speculations are connected in some way with a real physical theory, rather than airy fairy wiffle waffle.
 
  • #287
Kea said:
ZapperZ, there are clearly many of us working on similar ideas for QG, so banning it from this forum would be roughly the same as banning strings or LQG, which is to say, just ridiculous. Moreover, the mass matrices do in fact offer some evidence that these speculations are connected in some way with a real physical theory, rather than airy fairy wiffle waffle.

First of all, you are welcome to follow whatever development you want out of LQG. However, if ALL LQG community is doing is making analogy based on non-existent phenomena out of condensed matter physics, then I'd say the community needs to justify what they are doing using OTHER stuff. I would be shocked if they are using made-up principles as justification to base their analogies on. If you don't think there's anything wrong with this, then I'd say you have other bigger problems to deal with than me.

Secondly, if such "workings" are based on "established" line of research, then these "what if's" and are not "banned". The 'what if's" that I've referred to is when you are making such speculation based on an erroneous understanding of solid state physics or non-existent theory. This strategy makes no sense, even in LQG! I find it very hard to believe someone would do that with a straight face.

Remember what my original objection was. It was VERY specific!

I would also add that we have given discussions in this particular forum a lot of latitude that we would not allow in the other physics sub-forum. I'm fully aware of the nature of the subject matter in the fields being covered here and that's why certain requirement that are made in other physics areas are not strictly demanded in here. However, at some point, these freedom should not be abused or participants should not think that any wild speculation is allowed. Some degree of respect to our Guidelines should factor in in these posts.

Zz.
 
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  • #288
I am not put off by your objection, but I would have thought that my hypothesis that Neimeier "deep hole" lattice constructions as a way of looking at tesselated 24-dim spaces would have gotten maybe more criticism than this. The idea of a massive phonon is not initially that different than the Proca equations for a massive photon. Agreed these things don't exist in condensed matter states, but then again for these things we might "deform" the analogue. Zz just appears not to like this "deformation."

The standard model is a keyhole with which to peek into questions on cosmology and quantum gravity. Recent experimental finds at RHIC of gauge-balls or fireballs of quark-gluon plasmas with dual structures to black hole interiors suggests this is the case. Also the E_8 construction of elementary particles, where this has a lattice or sphere packing construction suggests on a theoretical level that we might be touching on some fundemantal issues of quantum gravity and cosmology.

Lawrence B. Crowell
 
  • #289
Lawrence B. Crowell said:
I am not put off by your objection, but I would have thought that my hypothesis that Neimeier "deep hole" lattice constructions as a way of looking at tesselated 24-dim spaces would have gotten maybe more criticism than this. The idea of a massive phonon is not initially that different than the Proca equations for a massive photon. Agreed these things don't exist in condensed matter states, but then again for these things we might "deform" the analogue. Zz just appears not to like this "deformation."

I'm not sure what you read out of the things that I've typed, but I have no issues with your "deformation". I only had issues when you invoke something that doesn't exist.

There are invalid analogies, and then there are valid analogies. When Peter Higgs invoked Nambu's analysis of how elementary particles can acquire mass using something analogous that he lnoticed out of the energy gap in a superconductor, that's a valid analogy. Why? Because they were citing something that's well-tested, verified, AND existed!

Again, in case this point was missed, as someone who was trained as a condensed matter physicist, I am THRILLED if other fields invoke stuff from what we work on. I have continued to trumpet some of the principles that came out of condensed matter physics (such as broken symmetries) that are now standard formulation in other areas of physics. However, these things should be done accurately. Making an analogy to something that doesn't exist simply makes no sense, at least to me. You are leaving yourself open for criticism (not to mention, ridicule), especially if you intend to have such ideas published. It is difficult enough when you have condensed matter Nobel Laureates such as Phil Anderson and Bob Laughlin questioning the worthiness of this area of study. I would think that the last thing you want to do is give them extra ammunitions by making faulty analogy or application of the field of study that they specialize in.

Zz.
 
  • #290
ZapperZ said:
I would be shocked if they are using made-up principles as justification to base their analogies on.

Clearly, you have completely misunderstood my position. You might want to read up a bit on what we are talking about before you start ranting on about its flaws. I am not a proponent of strings or LQG. In my opinion, these approaches lack motivating principles. So somebody makes a bad analogy...big deal! Surely it is more important to try and understand what they are saying.
 
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  • #291
Kea said:
Clearly, you have completely misunderstood my position. You might want to read up a bit on what we are talking about before you start ranting on about its flaws. I am not a proponent of strings or LQG. In my opinion, these approaches lack motivating principles.

.. and I think you have misunderstood my position even after I explained it a few times.

You will notice that I had issues with ONE particular post. I didn't come in here pointing flaws about what was being discussed here. However, you seem to think that I was trying to "ban" a whole slew of discussion. It was in reference to this claim of yours that I was asking for the rationality in not having any discomfort when an analogy was made to non-existent concepts.

How that somehow translates to my wanting to 'ban' the discussion, or how I was pointing out wholesale flaws to what was being discussed in this thread, that I haven't a clue.

Zz.
 
  • #292
ZapperZ said:
How that somehow translates to my wanting to 'ban' the discussion, or how I was pointing out wholesale flaws to what was being discussed in this thread, that I haven't a clue.

All right, my mistake. I was put off by the length of your input. If that's all you're saying, I agree, and the point could be made in one sentence.
 
  • #293
Kea said:
All right, my mistake. I was put off by the length of your input. If that's all you're saying, I agree, and the point could be made in one sentence.

My mistake. I thought I owe people an explanation for my point of view rather than simply saying "because I said so".

Zz.
 
  • #294
Carl: how are you going right now? Hope you're recovering.

It seems I have found 20 E8 roots which are capable of configuring all other three generations in a preon like style. I use 8 roots with "1/2" assignments and 12 with "1" assignments. All particles have a maximum of three preons, allthough I still have to check many of them one by one. This scheme facilitates that all quantum numbers for all the three generations turn out right. Does this make sense as far as you know?

NB: it looks like we have two parellel discussions in this thread.

Jan
 
  • #295
Berlin said:
Does this make sense as far as you know?

Suppose you got everything right. Do these elements form a group which are homeomorphic to those of the Standard Model?
 
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  • #296
Berlin said:
It seems I have found 20 E8 roots which are capable of configuring all other three generations in a preon like style. I use 8 roots with "1/2" assignments and 12 with "1" assignments. All particles have a maximum of three preons, allthough I still have to check many of them one by one.

I can hardly wait to see! If someone made me place bets, I would say 6 preons for each fermions, but they will arrive in pairs that are so tightly related that one could also call them 3 preons each. I should write up something on why this is the case, the short descrpition is that it makes it possible for weak hypercharge and weak isospin to be rotated by 45 degrees. On the bosons, I really don't know what to guess, maybe 4 preons each? 6? Surprise me, I can hardly wait.

My earlier comments on how to get preons into E8 through MUBs did turn out to be narcotics induced, or possibly just wrong, at least for the larger dimension Hilbert spaces. For dimension > 2 and 3, one needs to explore more general bases than those one would be restricted to by the MUB principle. I suppose you figured this out quickly.

For fitting E8, what I'd like to see would be quantum numbers for E8 that are not in the "eight 1/2s or 2 1s" form, which is very beautiful and symmetric, but instead quantum numbers with cubed roots of one. Then I think a preon structure for the generations would be more noticeable.

On the same topic, I typed up a "short" description of how Koide's formula comes from a preon model, since the stuff was in bits and pieces elsewhere:
http://carlbrannen.wordpress.com/2008/02/13/koide-formulas-and-qubit-qutrit-mubs/

Berlin said:
Carl: how are you going right now? Hope you're recovering.

Jan, I'm sufficiently recovered that I've been rough-housing with the guys again. The doctors are all very very good. And the nurses are all beautiful. And very very good. The food was also excellent, but all in all, I'm glad to be out.
 
  • #297
Solid state physics analogue

At the risk of creating a greater firestorm I will attempt to make the comparison with solid state physics and lattice based field theory more complete. I will work with the [itex]d_2~=~so(4)[/itex] and [itex]d_2~=~so(3,1)[/itex] electroweak and gravitational parts. The lattice will be the 24-cell or the [itex]\{3,~4,~3\}[/itex] polytope. The full E_8 theory of Lisi could be extended accordingly. The two [itex]d_2[/itex]'s combine into a graviweak [itex]d_4[/itex] with the combination of the 4 Higgs [itex]\phi[/itex] with the 4 vectors of gravitation into the 16 two-vectors [itex]e\phi[/itex] with a Clifford basis [itex]\Gamma_a~\in~Cl(7,~1)[/itex]

[tex]
\omega_{ew}~=~\frac{1}{2}\omega^{ab}_{ew}\Gamma_{ab},~e~=~e^a\Gamma_a,~\phi~=~\phi^a\Gamma_a,
[/tex]

for the electroweak, Higgs and gravitational frame connections respectively. The net graviweak connection is then

[tex]
A~=~\frac{1}{2}\omega~+~\frac{1}{4}e\phi~+~\omega_{ew}.
[/tex]

This define a curvature [itex]F~=~dA~+~(1/2)[A,~A][/itex]. In the BF theory the Lagrangian is [itex]{\cal L}~=~B\cdot F[/itex].

The extension to solid state physics is seen if the hamiltonian is written in the compact form

[tex]
H~=~AA~\rightarrow~\alpha\sigma\cdot k,
[/tex]

for [itex]\sigma[/itex] an effective spin from the Grassmannian B-form, and [itex]\alpha[/itex] a constant. The wave function for this Hamiltonian [itex]\psi~=~|\psi|e^{i\Phi}[/itex] and Green's function [itex]G(k,~\omega)~=~1/(k~-~k_F~-~i\omega)e^{i\Phi}[/itex], where [itex]\omega[/itex] is a frequency determined by a dispersion relationship. This Green's function is for k-vectors pointing radially away from a Fermi surface, or a heghog condition. The condition on the [itex]k_F[/itex] may be determined by the Higgs vev as seen in equation 3.8 of Garrett Lisi's paper, or by an orbifold compactification in a way similar to what I illustrated in post # 72.

The idea is then that QFT has a fermionic and bosonic component with [itex]E~\sim~ck^4[/itex], which for [itex]k~=~1/L_p[/itex] determines a large ZPE term. Yet if for [itex]E~=~(N_B~-~N_F)ck^4[/itex] the cosmological problem can be worked on in this format. There may be a tower of mass states which appropriately cancel at all scales so that the cosmological constant is not so horridly large.

Lawrence B. Crowell
 
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  • #298
Aside

The mathematician Kostant has been talking to Baez and others about Lisi's paper.

http://web.mit.edu/mikihavl/www/LG/abstracts07/kostant.pdf
 
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  • #299
Kea said:
The mathematician Kostant has been talking to Baez and others about Lisi's paper.

How do you know he's talking to them? Any source? That pdf just says he is talking about Lisi's paper.
 
  • #300
Whoa, that's great. Bertram Kostant is one of the world's greatest experts on Lie groups, and specifically the structure of E8. It was a conversation between him and John Baez that led John to make the post on E8 that I read and first realized the implications for the unification I was attempting:
http://math.ucr.edu/home/baez/week90.html

I'd be very curious to hear what he has to say during that MIT talk -- does anyone know if these things are available online? It doesn't appear so.
 
  • #301
Perhaps you can go - it looks like it's at UC San Diego this Sunday
http://www.math.ucsd.edu/announcements/seminars/
 
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  • #302
Ha!

That's highly amusing. He'll be talking about this at the same place where I learned differential geometry.

I'm not going to be able to make it though, as I'm up by Lake Tahoe right now.
 
  • #303
I guess I have to ask again... Why just finding a suitable combination of the E(8) roots in a preon fashion suficient to reproduce the standard model group? I don't see the reason in that.
 
  • #304
According to various web pages
Kostant gave a talk with the same title
"On some mathematical of the background to Garrett Lisi's " E(8) Theory of Everything"
and the same abstract
"A physicist , Garrett Lisi, has published a highly controversal, but fascinating, paper purporting to go beyond the standard model in that it unifies all 4 forces of nature by using as gauge group the exceptional Lie group E(8). My talk, strictly mathematical, will be about an elabloration of the mathematics of E(8) which Lisi relies on to construct his theory."

at UC Riverside (John Baez's institution) on 12 February 2008,
and
as Kea said is to give a talk on the same title/abstract at MIT on 5 March 2008
and
as FredA2 said is to give a talk on the same title/abstract at UCSD on 17 February 2008.

However, I have yet to see a paper or set of slides or any other record of details of what Kostant may be saying.

Tony Smith
 
  • #305
MTd2 said:
I guess I have to ask again... Why just finding a suitable combination of the E(8) roots in a preon fashion suficient to reproduce the standard model group? I don't see the reason in that.

I down loaded your pdf file on preon states. It appears incomplete as yet.

Correct me if I am wrong, for I don't know that much about preons, but these are putative subparticle states of quarks and leptons as I understand. There is another class of such theories which posit particle states called rishons which are sub-quarks and sub-lepton states.

The problem that seems to exist with these ideas is that the binding energy for such particle states is going to be inordinately large. For instance with the electron in the H-atom the binding energy is -13.7 ev, and for nucleons in a nucleus binding energy is in the 10 Mev range. For quarks in a hadron "bag" the binding energy has a magnitude comparable to the masses of the quarks. If one assumes that quarks and leptons are composed of further particles this would seem to give considerable difficulty in understanding such bound states --- in particular with renormalization issues.

Also with the electron very sensitive measurements have been performed on the Lande' g-factor, where of course corrections from g = 2 are predicted by QED. There continues to be a physics industry to measure this to ever higher orders and people compute higher order Feynman diagrams. I think the effort is up to O([itex]\alpha^{10}[/itex]) or so. So far things, as I understand them, indicates the electron as is point-like with no "warts" or substructure detected.

Lawrence B. Crowell
 
  • #306
Lawrence B. Crowell said:
I down loaded your pdf file on preon states. It appears incomplete as yet.

I didn't upload any file... I am still studying the underlying stuff so that I can come up with something. I am reading this thread and getting tips on what I must study.
 
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  • #307
Well, anyway, I just want to know about E(8) 4-manifolds. There is still a road ahead to understand it. It was the 1st example of a non triangulable manifold. It's interesting because it looks like a totaly empty space, from the point of view of an observer. I am not sure, since I didnt study it, but that means you have potentials, but no way to measure them. You don't have how to define stoke or gauss law, i think, since you wouldn't have homology or cohomology groups, so you can't measure any kind of flux. So, maybe you can't make an experiment or observation. Maybe no interection. That manifold would be like a virtual reality space, or a dead speace, or a white blank space.
 
  • #308
MTd2 said:
I didn't upload any file... I am still studying the underlying stuff so that I can come up with something. I am reading this thread and getting tips on what I must study.

Sorry, I think the file was by "Berlin."

L. C.
 
  • #309
Wondering what had been said in arXiv papers about Garrett's paper 0711.0770, I did a citebase search and found 4 papers citing Garrett's paper:

1 - 0711.3248 [hep-th] by Tibra Ali and Gerald B. Cleaver of Baylor University, in which they said
"... In passing we note that the decomposition of the ‘visible’ E8 in terms of F4 and G2, which naturally comes out of HF manifolds, is reminiscent of the group-structure of the unification scenario recently proposed by Lisi ...".

2 - 0712.0946 [hep-th] by A. Morzov of ITEP, in which he said
"... higher derivative terms are indeed present in most approaches, from
QFT formulations of string and M-theory to pure QFT models like asymptotically safe gravity or (the quantum version of) the recent E8 unification model [Garrett's paper]...".

3 - 0712.0977 [hep-th] by Lee Smolin of the Perimeter Institute, in which he said
"... We study a unification of gravity with Yang-Mills fields based on a simple exten-
sion of the Plebanski action to a Lie group G which contains the local lorentz group.
... This may be applied to Lisi’s proposal of an E8 unified theory, giving a fully E8 invariant action.
The extended form of the Plebanski action suggests a new class of spin foam
models. ...
Lisi’s proposal breaks the gauge invariance ... by a strategy of incorporate fermions by means a BRST extension of the connection. ... I propose an alternative way to incorporate the fermions, which would not break the gauge symmetry. ...
There are also open issues regarding spin and statistics; these may be addressed by generalized or topological spin-statistics theorems. ...".

4 - 0712.2976 [hep-th] by Massimo Bianchi and Sergio Ferrara of the CERN Physics Theory Unit, in which they said
"... the group E8(−24) ... is the exceptional group used in ...[Garrett's paper]... in a (hopeless) attempt to unify gravity with the Standard Model. ...".

Papers 1 and 2 just mention Garrett's model in passing, without evaluating it, which is in my opinion reasonable.

Paper 3 by Smolin goes into some detail about how Garrett's model might be a basis for useful physics, and also seems to me to be reasonable.

Paper 4 by Bianchi and Ferrara of CERN would be like 1 and 2 except for the gratuitous and unsupported word "hopeless".
If their paper is to be considered to be a serious physics paper (it was allowed on hep-th in the Cornell arXiv), then it seems to me that if they allege that something (such as Garrett's paper) is "hopeless" then they should give a detailed physics argument that Garrett (or anyone else) could rebut in detail.
In my opinion what they did was disgraceful,
and they should either withdraw the "hopeless" word and apologize
or put up a paper that supports their allegation of hopelessness in detail so that it can be rebutted.

Tony Smith
 
  • #310
I have hope.
in other words:
yes we can.
 
  • #311
Tony Smith said:
3 - 0712.0977 [hep-th] by Lee Smolin of the Perimeter Institute, in which he said
"... We study a unification of gravity with Yang-Mills fields based on a simple exten-
sion of the Plebanski action to a Lie group G which contains the local lorentz group.
... This may be applied to Lisi’s proposal of an E8 unified theory, giving a fully E8 invariant action.
The extended form of the Plebanski action suggests a new class of spin foam
models. ...
Lisi’s proposal breaks the gauge invariance ... by a strategy of incorporate fermions by means a BRST extension of the connection. ... I propose an alternative way to incorporate the fermions, which would not break the gauge symmetry. ...
There are also open issues regarding spin and statistics; these may be addressed by generalized or topological spin-statistics theorems. ...".

Tony Smith

Smolin's action, Plebanski's action, in equation 1 ( 0712.0977 [hep-th] ) is formally similar to equation 3.7 in Garrett's paper, or the gravitational action further down from 3.7. The gauge fields in the theory come from G/SO(4), where the Euclideanized gravity has been "moded out." From the nature of the action employed this theory should be similar to the Exceptional E_8 simplicity.

Smolin's idea of BRST quantization, presumably on supergenerators, I agree with in principle. It is best to have Fermion in the theory by topological means, eg [itex]Q^2~=~{\bar Q}^2=~0[/itex] and states [itex]\psi~=~{\bar Q}\chi[/itex]. However, SUSY is broken and we have to contend with the issue of the vev. This is in part an interest in my "trial balloon" with a tower of masses for particles in a solid state physics-like model, but where even with broken SUSY we have a small vev.

Lawrence B. Crowell
 
  • #312
Tony Smith said:
Wondering what had been said in arXiv papers about Garrett's paper 0711.0770, I did a citebase search and found 4 papers citing Garrett's paper:

Have you talked to anyone at Georgia Tech about Garrett's paper or your paper based on Garrett's paper?
 
  • #313
John G asked "... Have you talked to anyone at Georgia Tech about Garrett's paper or your paper based on Garrett's paper? ...".

Yes. Back in January 2008 I sent an email to David Finkelstein, who is physics professor emeritus at Georgia Tech, saying in part

"... when Garrett Lisi's E8 model at http://arxiv.org/abs/0711.0770
came out in November 2007 you [David] were quoted by the London Telegraph as saying "... Some incredibly beautiful stuff falls out of Lisi's theory ... This must be more than coincidence and he really is touching on something profound. ...".
Since then,
I have been working on a formulation of my [Tony's] physics model in terms of E8 ...".

Pursuant to that, we had lunch. My understanding of the substance of what David Finkelstein said is:
1 - David had heard Garrett talk in Iceland around August 2007 and was favorably impressed at that time;
2 - David regretted giving the quoted comments to the reporter;
3 - David now (at the time of lunch last month) was not favorably impressed with Garrett's E8 model;
4 - David now was skeptical about anything being a TOE;
5 - For physics model-building, David said that he preferred SO(16) to E8.

I mentioned to David that E8 = adjoint of SO(16) + half-spinor of SO(16)
and David seemed interested in that point, and I gave David a paper copy of my E8 paper at
http://tony5m17h.net/GLE8Cl8TSxtnd.pdf
which contains some discussion about that point.

I have not heard from David since the day we ate lunch, 23 January 2008.

I don't know of anyone else at Georgia Tech who might have any serious interest in Garrett's E8 work or my work.

Tony Smith
 
  • #314
I just checked the web and found that the "around August 2007" Iceland conference at which David Finkelstein heard Garrett Lisi was according to Garrett's CV web page at
http://sifter.org/~aglisi/Physics/CV.html

"... FQXi 2007 Inaugural Conference, 5/21-5/26/2007, Reykjavik, Iceland.
[Garrett's] Contributed talk: "The Universe as a Pretty Shape" ...".

Tony Smith
 
  • #315
Tony Smith said:
According to various web pages
Kostant gave a talk with the same title
"On some mathematical of the background to Garrett Lisi's " E(8) Theory of Everything"
and the same abstract
"A physicist , Garrett Lisi, has published a highly controversal, but fascinating, paper purporting to go beyond the standard model in that it unifies all 4 forces of nature by using as gauge group the exceptional Lie group E(8). My talk, strictly mathematical, will be about an elabloration of the mathematics of E(8) which Lisi relies on to construct his theory."

at UC Riverside (John Baez's institution) on 12 February 2008,
and
as Kea said is to give a talk on the same title/abstract at MIT on 5 March 2008
and
as FredA2 said is to give a talk on the same title/abstract at UCSD on 17 February 2008.

However, I have yet to see a paper or set of slides or any other record of details of what Kostant may be saying.

Tony Smith


If anyone finds anymore information about what his talk included and any reactions to it, id be very intrigued to hear it, as I'm sure Garret is.
 

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