Tony, I really need your help on this one:
http://arxiv.org/PS_cache/arxiv/pdf/0711/0711.0770v1.pdf
Am I correctly reading this as the quark spinors being a harmonic of the electron spin frequency?
 
Fitz

Hi Fitz!
 
Well Visi is definitely on the right track with the E8 Lie Group and the octonion symmetry.  The universe reduces (or begins to manifest) to mathematical abstraction first;  then emerges a holographic principle in manifesting a metric background as a 4D-flat Minkowski spacetime and thirdly energizes this background in quantizing and magnifying those elementary quantum geometric templates.
 
As said before this is well studied and underpins heterotic superstring theory. My point is, that the 'missing' particles and connections of this supergeometry derived in the above link (many pictures of the E 8 symmetry are 2D mapped there) always engage this 8-symmetry.
For example the 57 dimensions are of course 56+1 and the 240 are 30x8 and so forth. I am in no manner capable to explain the Visi paper to you; my technical expertise on the symbolism is inadequate for that; but I can simplify the structure a little.
 
You have 8 gluons, which I reduce to just one (or two for spin chirality) in not labelling the gluons as 1,2,3,..8, but allowing a geometric trisection (this is the triune labelling in the Visi paper) of a minimum geometric circle say.
Then there are 8 colour permutations, which we may label as E=mc^2 for B(lack) in inertial mass and as E=hf for W(hite) in gravitational or photonic mass: mc^2=BBB; BBW; BWB; WBB; WWB; WBW; BWW and WWW=hf.
 
So the gluonic eigenstates become eigenstates of gluonic quantum geoemtry and are one of the 8 vertex lines in the Visi E8 model say generalised.
 
Then you have precisely 8 diquark families: {U=uu; D=dd; S=ss; b=ud; m=us; t=ds}
UP/DOWN Level: uu(bar); ud(bar); du(bar) are PIONS about 150 MeV;
STRANGE Level:  us(bar) and su(bar) are KAONS about 490 MeV;
CHARM Level:     Uu(bar) are the semistates for the J/PSI's of so 1600 MeV (see pentaquarks);   
BEAUTY Level:    bu(bar); b(bar)u are the semistates for the UPSILONS at so 5200 MeV;
MAGIC Level:      mu(bar); m(bar)u are the (suppressed) semistates for EPSILONS at 17100 MeV;
DAINTY Level:     Dd(bar); D(bar)d are the (suppressed) semistates for OMICRONS at 56000 MeV;
TRUTH Level:      td(bar); t(bar)d are the semistates for the KOPPAS at 183000 MeV;
SUPER Level:     Ss(bar); S(bar)s are the suppressed semistates for the HIGGS/CHIS at 597000 MeV.
 
There is a quark singlet in the Charm a quark doublet in the Beauty/Magic and a quark triplet in the Dainty/Truth/Super with ony the Charm, the Beauty and the Truth manifesing.
 
So the Visi paper derives this elementary symmetry in technical detail using quantum field theory and the 4D metric.
Now the interesting thing is that once one eliminates this metric, then one gets a demetricated background of the quantum foam or the quantum lattice connections of Smolin and Ashtekar say.
So the pieces fit in in my statement of reducing the physics to quantum geometry and ending in say algorithms of binary code of the opening and closing of superstring as say the 'Planck-Connectors'.
 
So one must by necessity arrive at some complex geometry symbolising this in the observed natural phenomena.
 
Your idea of quarks spinning harmonically with electrons holds, but only superfically or peripherally.
Once one reduces everything to chirality in 26(x7) dimensions of a Bosonic String (this is also in the Visi paper) and then allows chiralities to enter in defining various superstring scenarios in classes; then this E(8x8) structure emerges for a class E(8x8) in modular duality with the other classes: Planck/I; Monopole/IIB; XL-Boson/HO(32); E-Boson(Cosmic Ray Ankle)/IIA and materialising wormhole EpsEss/HE(64).
 
Visi basically rewrites the Standard Model symmetries in an extended form, which imo incorporates the 'missing' diquarks outlined above (I labeled the Dainty, Magic and Super and the Omicron, Epsilon and Koppa and Higgs/Chi, the others are standard).
 
Also this unification of the gauges (in say Visi's incorporation of the Einstein tensors) in the action terms so also can be seen in geometric terms. Visi basically allows mass to become absolved in say extended action in coupling the classical geometry of Einstein with geometry of quantums using 240, 57-1, 57+1 and 7x26=182 dimensions to embed the 3+1 spacetime as topological mappings connecting the dimensions as vertex couplings or what have you.
 
So I basically see where this mathematics might lead to in the unification physics; but my mathematical understanding is not deep enough to elaborate much further.
I advise anyone interested to study up on octonions (say the Baez papers) to gain more understanding about the technical tools used by Visi.
 
But your resonances relate imo to the coupling between the kernel-quarks, defining the baryons, hyperons and their resonances; with the ring-leptons (electron, muon, taus and resonances(?)) and not to a basic spinor elementary eigenstate.
Both leptons and baryons (nucleons) derived from a bifurcation of the class HO(32=4x8) heterotic superstring class, which is directly dual to the 64-class. My argument with the string experts is, that those five classes are NOT at the same Planck-Energy level but form a hierarchy ending in the HE-64 class which manifests the kernel of the Higgs Boson in a neutrino-gluon coupling as a strongweak unification of the inertial mass eigenstates.
Then the massless photon-graviton selfstates couple to the strongweak unification in manifesting the wormhole under the auspices of the HE(8x8) superstring symmetry.
 
 
Tony B.
 

Is this the fabric of the universe? Last Updated: 12:01am GMT 19/03/2007

Roger Highfield describes a heroic mathematical enterprise that could lay bare the fundamentals of the cosmos Mathematicians have successfully scaled their equivalent of Mount Everest. Today they unveil the answer to a problem that, if written out in tiny print, would cover an area the size of Manhattan.   A two dimensional representation of E8, courtesy of Peter McMullen and John Stembridge At the most basic level, the calculation is an arcane investigation of symmetry – in this case of an object that is 57 dimensional, rather than the usual three dimensional ones that we are familiar with. Although this object was first discovered in the 19th century. there is evidence that it could contain the structure of the cosmos. Mathematicians are known for their solitary style of working, but the combined assault on what is described as "one of the largest and most complicated structures in mathematics" required the effort of 18 mathematicians from America and Europe for an intensive four-year collaboration. The feat may baffle most people but could have unforeseen implications in mathematics and physics, which won’t be evident for years to come, said the American Institute of Mathematics. "The group of symmetries of this strange geometry called E8 is one of the most intriguing structures that Nature has left for the mathematician to play with," commented Prof Marcus du Sautoy of Oxford University, currently in Auckland. "Most of the time mathematical objects fit into nice patterns that we can order and classify. But this one just sits there like a huge Everest."   What makes this group of symmetries so exciting is that Nature also seems to have embedded it at the heart of many bits of physics. One interpretation of why we have such a quirky list of fundamental particles is because they all result from different facets of the strange symmetries of E8. I find it rather extraordinary that of all the symmetries that mathematicians have discovered, it is this exotic exceptional object that Nature has used to build the fabric of the universe. The symmetries are so intricate and complex that today’s announcement of the complete mapping of E8 is a significant moment in our exploration of symmetry." For the feat, the team used a mix of theoretical mathematics and intricate computer programming to successfully map E8, (pronounced "E eight") which is an example of a Lie (pronounced "Lee") group. Lie groups were invented by the 19th century Norwegian mathematician Sophus Lie to study symmetry. Underlying any symmetrical object, such as a sphere, is a Lie group. Balls, cylinders or cones are familiar examples of symmetric three-dimensional objects. Today’s feat rests on the drive by mathematicians to study symmetries in higher dimensions. E8 is the symmetries of a geometric object that is 57-dimensional. E8 itself is 248-dimensional. "E8 was discovered over a century ago, in 1887, and until now, no one thought the structure could ever be understood," said Prof Jeffrey Adams, Project Leader, at the University of Maryland. "This groundbreaking achievement is significant both as an advance in basic knowledge, as well as a major advance in the use of large scale computing to solve complicated mathematical problems." "This is an exciting breakthrough," said Prof Peter Sarnak at Princeton University. "Understanding and classifying the representations of E8 and Lie groups has been critical to understanding phenomena in many different areas of mathematics and science including algebra, geometry, number theory, physics and chemistry. This project will be invaluable for future mathematicians and scientists." The ways that E8 manifests itself as a symmetry group are called representations. The goal is to describe all the possible representations of E8. These representations are extremely complicated, but mathematicians describe them in terms of basic building blocks. The new result is a complete list of these building blocks for the representations of E8, and a precise description of the relations between them, all encoded in a matrix, or grid, with 453,060 rows and columns. There are 205,263,363,600 entries in all, each a mathematical expression called a polynomial. If each entry was written in a one inch square, then the entire matrix would measure more than seven miles on each side. The result of the E8 calculation, which contains all the information about E8 and its representations, is 60 gigabytes in size. This is enough to store 45 days of continuous music in MP3-format. If written out on paper, the answer would cover an area the size of Manhattan. The computation required sophisticated new mathematical techniques and computing power not available even a few years ago. "This is an impressive achievement," said Hermann Nicolai, Director of the Albert Einstein Institute in Potsdam, Germany. "While mathematicians have known for a long time about the beauty and the uniqueness of E8, we physicists have come to appreciate its exceptional role only more recently - yet, in our attempts to unify gravity with the other fundamental forces into a consistent theory of quantum gravity, we now encounter it at almost every corner," he said, referring to efforts to combine the theory of the very big (general relativity) with the very small (quantum mechanics). "Thus, understanding the inner workings of E8 is not only a great advance for pure mathematics, but may also help physicists in their quest for a unified theory."

 
Tony B. says:
 
The Heterotic Superstring HE(8x8) is based upon this symmetry and Quantum Relativity has for over 10 years now claimed that the last and final Planck String transformation gives the EpsEss Supermembrane with eigenfrequency 3x10^30 Hz for an eigenenergy of so 1.24x10^7 GigaEletronVolts. It is this selfstate, which rtranslates to the wormhole perimeter of 10^-22 metres and which can be approached in the subatomic particle accelerator experiments from above.
So certain neutrino-gluon gauge interactions should become apparent in the proposed LHC experiments of Geneva.
 
I doubt however, that the graviton-photon interaction will be discovered at the lower energies. A concentrated energy of 0.002 Joules concentrated in a cross-sectional interaction area of almost 8x10^-46 squaremetres should however manifest the wormhole at the centre of the graph above.
 
Tony B.

A Theoretically Simple Exception of Everything

Garrett Lisi, who was featured in our inspiration series back in August, has a new paper on the arxiv about his recent work

An Exceptionally Simple Theory of Everything
arXiv: 0711.0770

I met Garrett at the Loops '07 in Morelia, and invited him to PI. He gave a talk here in October, which confirmed my theory that the interest in a seminar is inversely proportional to the number of words in the abstract. In his case the abstract read: "All fields of the standard model and gravity are unified as an E8 principal bundle connection," and during my time at PI it was the best attended Quantum Gravity seminar I've been at.

Anyway, since I've spend some time trying to understand what he's been doing (famously referred to as 'kicking his baby in the head') here is a brief summary of my thoughts on the matter.

Preliminaries

In the 50's physicists were faced with a confusing, and still growing multitude of particles. By introducing new quantum numbers, it was clear that this particle zoo exhibited some kind of pattern. Murray Gell-Mann realized the particles could be classified using the mathematics of Lie-groups. More specifically, he found that the baryons with spin 3/2 known at this time correspond to the weight diagram of the ten-dimensional representation of the group SU(3) [1].

He matched the nine known spin 3/2 baryons (4 Δs, 3 Σ*s, 2 Ξ*s) with the weights of this representation, but there was one particle missing in the pyramid. He therefore predicted a new particle, named Ω-, which was later discovered and had the correct quantum numbers to complete the diagram [2]. Because of the ten baryons in the multiplet, this is also known as the 'baryon decuplet'.

A similar prediction could later be made for the baryon octet, where the center of the diagram should be doubly occupied. The existence of the missing Σ⁰ was later experimentally confirmed.

After this, the use of symmetry groups to describe nature has repeatedly proven to be an enormously powerful and successful tool. Besides being useful, it is also aesthetically appealing since the symmetry of these diagrams is often perceived as beautiful [3].

GUTs and TOEs

Today we are again facing a confusing multitude of particles, though on a more elementary level. The number of what we now believe are elementary particles hasn't grown for a while, but who knows what the LHC will discover? Given the previous successes with symmetry principles, it is only natural to try to explain the presently known particles in the standard model - their families, generations, and quantum numbers - as arising from some larger symmetry group in a Grand Unified Theory (GUT). One can do so in many ways; typically these models predict new particles, and so far unobserved features like proton decay and lepton number violation. This larger symmetry has to be broken at some high mass scale, leaving us with our present day observations.

Today's Standard Model of particle physics (SM) is based on a local SU(3)xSU(2)xU(1) gauge symmetry (with some additional complications like chirality and symmetry breaking). Unifying the electroweak and strong interaction would be great to begin with, but even then there is still gravity, the mysterious outsider. A theory which would also achieve the incorporation of gravity is often modestly called a 'Theory of Everything' (TOE). Such a theory would hopefully answer what presently is the top question in theoretical physics: how do we quantize gravity? It is also believed that a TOE would help us address other problems, like the observed value of the cosmological constant, why the gravitational interaction is so weak, or how to deal with singularities that classical general relativity (GR) predicts.

Commonly, gravity is thought of as an effect of geometry - the curvature of the space-time we live in. The problem with gravity is then that its symmetry transformations are tied to this space-time. A gauge transformations is 'local' with respect to the space-time coordinates (they are a function of x), but the transformations in space-time are not 'local' with respect to the position in the fibre, i.e. the Lie-Group. That is to say, usually a gauge transformation can be performed without inducing a Lorentz transformation. But besides this, the behavior of particles under rotations and boosts - depending on whether dealing with a vector, spinor or tensor - looks pretty much like a gauge transformation.

Therefore, people have tried to base gravity on an equal footing with the other interactions by either describing both as geometry, both as a gauge theory, or both as something completely different. Kaluza-Klein theory e.g. is an approach to unify GR with gauge theories. This works very nicely for the vector fields, but the difficulty is to get the fermions in. So far I thought there are two ways out of this situation. Either add dimensions where the coordinates have weird properties and make your theory supersymmetric to get a fermion for every boson. Or start by building up everything of fermionic fields.

Exceptional Simplicity

On the algebraic level the problem is that fermions are defined through the fundamental representation of the gauge group, whereas the gauge fields transform under the adjoint representation. Now I learned from Garrett that the five exceptional Lie-groups have the remarkable property that the adjoint action of a subgroup is the fundamental subgroup action on other parts of the group. This then offers the possibility to arrange both, the fermions as well as the gauge fields, in the Lie algebra and root diagram of a single group. Thus, Garret has a third way to address the fermionic problem, using the exceptionality of E8.

His paper consists of two parts. The first is an examination of the root diagram of E8. He shows in detail how this diagram can be decomposed such that it reproduces the quantum numbers of the SM, plus quantum numbers that can be used to label the behaviour under Lorentz transformations. He finds a few additional particles that are new, which are colored scalar fields. This is cute, and I really like this part. He unifies the SM with gravity while causing only a minimum amount of extra clutter. Plus, his plots are pretty. Note how much effort he put in the color coding!

Garrett calls his particle classification the "periodic table of the standard model". The video below shows projections of various rotations of the E8 root system in eight dimensions (see here for a Quicktime movie with better resolution ~10.5 MB)

[Each root of the E8 Lie algebra corresponds to an elementary particle field, including the gravitational (green circles), electroweak (yellow circles), and strong gauge fields (blue circles), the frame-Higgs (squares), and three generations of leptons (yellow and gray triangles) and quarks (rbg triangles) related by triality (lines). Spinning this root system in eight dimensions shows the F4 and G2 subalgebras.]

However, just from the root diagram alone it is not clear whether the additional quantum numbers actually have something to do with gravity, or whether they are just some other additional properties. To answer this question, one needs to tie the symmetry to the base manifold and identify part of the structure with the behaviour under Lorentz transformations. A manifold can have a lot of bundles over it, but the tangential bundle is a special one that comes with the manifold, and one needs to identify the appropriate part of the E8 symmetry with the local Lorentz symmetry in the tangential space. The additional complication is that Garrett has identified an SO(3,1) subgroup, but without breaking the symmetry one doesn't have a direct product of this subgroup with additional symmetries - meaning that gauge transformations mix with Lorentz-transformations.

Garrett provides the missing ingredient in the second part of the paper where he writes down an action that does exactly this. After he addressed the algebraical problem of the fermions being different in the first part, he now attacks the dynamical problem with the fermions: they are different because their action is - unlike that of the gauge fields - not quadratic in the derivatives. As much as I like the first part, I find this construction neither simple nor particularly beautiful. That is to say, I admittedly don't understand why it works. Nevertheless, with the chosen action he is able to reproduce the adequate equations of motion.

This is without doubt cool: He has a theory that contains gravity as well as the other interactions of the SM. Given that he has to choose the action by hand to reproduce the SM, one can debate how natural this actually is. However, for me the question remains which problem he can address at this stage. He neither can say anything about the quantization of gravity, renormalizability, nor about the hierarchy problem. When it comes to the cosmological constant, it seems for his theory to work he needs it to be the size of about the Higgs vev, i.e. roughly 12 orders of magnitude too large. (And this is not the common problem with the too large quantum corrections, but actually the constant appearing in the Lagrangian.)

To make predictions with this model, one first needs to find a mechanism for symmetry breaking which is likely to become very involved. I think these two points, the cosmological constant and the symmetry breaking, are the biggest obstacles on the way to making actual predictions [4].

Bottomline

Now I find it hard to make up my mind on Garrett's model because the attractive and the unattractive features seem to balance each other. To me, the most attractive feature is the way he uses the exceptional Lie-groups to get the fermions together with the bosons. The most unattractive feature are the extra assumptions he needs to write down an action that gives the correct equations of motion. So, my opinion on Garrett's work has been flip-flopping since I learned of it.

So far, I admittedly can't hear what Lee referred to in his book as 'the ring of truth'. But maybe that's just because my BlackBerry is beeping all the time. And then there's all the algebra clogging my ears. I think Garrett's paper has the potential to become a very important contribution, and his approach is worth further examination.

Aside: I've complained repeatedly, and fruitlessly, about the absence of coupling constants throughout the paper, and want to use the opportunity to complain one more time.

For more info: Check Garrett's Wiki or his homepage.