GroupT

E8 theory

Hi GT, I uploaded digrams at User:Tomruen/aestoe from the Dec 2010 article, and pasted your comments about them from the An exceptionally simple theory of everything talk page. As I said before, I'd like some diagrams like these added to the article, but since I'm still learning about what it all means, I'm content to wait a while, until I can better assess how the diagrams can be interelated to the existing physics and math articles on wikipedia. Hopefully when I make a new attempt at the first diagram, you can help me again sort out the uncertainties. Thanks! Tom Ruen (talk) 02:04, 14 January 2012 (UTC)

File:Gta-3.png

Your comments: 2) This is also a correct picture. This is actually one of the most interesting pictures of all, IMHO. There are these very very nice papers, published in 2002 Exceptional Confinement in G(2) Gauge Theory http://arxiv.org/abs/hep-lat/0209093 (Journal reference: Nucl.Phys. B668 (2003) 207-236) and 2003 Confinement without a center: the exceptional group G(2) http://arxiv.org/abs/hep-lat/0302023v1 (Published in Nucl.Phys.Proc.Suppl. 119 (2003) 652-654). They not only have the same identical picture as Lisi, but they even specifically recall the weight diagrams to compare the group SU(3) and the 3 and the 3bar and their relation to SO(7) and G2 (like I was saying above). But Lisi doesn't even cite them! (of course, he thinks he's the first one to use these diagrams...) By the way, those authors all have 1000 citations or more (and the two papers together have about 60 citations, they should have been cited by Lisi). To explain: they try to use G2 and its fundamental representation 7, breaking the symmetry at a high scale, to prove how the 7 would naturally break into the 3 and the 3bar (which in their picture is natural once the bosons that move from the 3 to the 3bar become very massive). Of course it's not a TOE and their approach is different, but they even look, in their second paper, at the possibility of having G2 usually nonchiral gauginos (gluinos) as chiral fermions. Being a supersymmetric theory of course they look at the chirality issue of the gauginos and attempt a domain-wall/string-theory-like approach. This issue, far from being easy to solve, as I've been mentioning here for months, is pretty common in supersymmetric models when dealing with gauginos and their chirality.

B₃ or SO(7) weight diagram as a cuboctahedron, with a central A₂ or SU(3) hexagon and 2 dual triangles above/below

Thanks for those papers showing G2. I don't know enough to easily compare what they're plotting, but Lisi's 2007 paper makes it clear - 6 gluons on the outer hexagon, and 6 quark/antiquark color combinations on the inner hexagram. Are you saying these papers weight diagrams are intended represent these same particles? ALSO, the first [1] has two figures, first with a 7-dimensional fundamental representation of G(2), and second a 14-dimensional adjoint representation of G(2), with both the long and short roots of G₂. Can you explain this? What is a fundamental representation? It would seem accurate to call Lisi's G3/G8 projective plane Color charge diagram - AND that a diagram like one of these deserves to be there? I also see at Gluon#Eight_gluon_colors that there are 8 gluons, while this chart only shows 6. Tom Ruen (talk) 00:59, 15 January 2012 (UTC)

Busy couple of days, I'll try to respond tonight or tomorrow, at least briefly. ~GT~ (talk) 04:38, 15 January 2012 (UTC)

I found some clarity, still more to learn... G₂ symmetry is broken into A₂ or SU(3) subgroup, which holds the 8 gluons, 6 as root vectors, and 2 more as generators. Lisi's original paper showed only 6, while the SciAm article shows all 8, as the caption says, with last two overlapping in the middle. Also G₂ is a subgroup of B₃ or SO(7), which has the same 12 roots, in the vertex arrangement of a cuboctahedron. Lisi's original paper, Table 2 shows a third charge direction he calls B2, where the up and down quarks have opposite charges, and gluons sit at zero in that charge. He doesn't have a diagram of the 3D cuboctahedron, but he describes it in the text. Tom Ruen (talk) 19:42, 16 January 2012 (UTC)

OK, so here is my doubts about this. I'm not sure about what you are asking, but what you say above seems reasonable, except that those cannot be quarks in the arrangement proposed by Lisi. The problem is that it doesn't make any sense to describe the quarks in a G2 (or even SO(7) way if you want to include some sort of U(1) hyper charge), unless you explain how it is possible that the 14 points in the diagrams, that are all vector bosons, can become fermions (this might need a longer explanation but for now let's keep it short). Now, the paper that I mentioned tried to include fundamental representations of G2, in that case they are more conservative and study the 7 and the 14, if I recall correctly (I should check), the problem with those can also be discussed. The other approach they used is a supersymmetric approach, doubling all the particles so that for each gluon there was also a gluino, and tried some other technique to make those chiral. The problem with this last approach, more similar to what Lisi does, is that by construction all these gluinos have to be neutral under any other charge (otherwise the initial G2 symmetry would be explicitely broken). Lisi is trying to solve this including the weak interaction and gravity in the picture, which could be a good idea, except nothing of what he's tried has worked so far or can work at all (see D-G theorem). Showing such a diagram would not be a correct physics statement, and the readers would just be confused, because an appealing and catchy diagram is shown, but you need too much information to understand that the diagram itself isn't really correct, and if you just look at the charges, then we should do the same thing for all the unified theories, showing that all show similar patterns. I think that the best we can do for wikipedia is to start using some of these diagrams (and you have a very good collection of them) in the unification pages. Otherwise I think that it's hopeless to include those in Lisi's theory's page without having issues with WP:UNDUE and WP:No original research. But to answer a question you raised above, yes, Lisi used the same identification for the quantum numbers that was used in those papers, but he forgot to cite them, both for the idea and for the visualization. ~GT~ (talk) 20:56, 22 January 2012 (UTC)

I think we're in agreement, ideally show diagrams in the standard model articles where they are citable with standard interpretations and labels and all, and any specific unification models (including Lisi's) which make assumptions beyond the standard model, including Lisi's E8 model, may include their own diagram/visualizations, if appropriate and helpful to readers. The issue I'm exploring now is how groups are decomposed, like Lie_group_decomposition I guess, since my diagrams are "full groups", working only on the semisimple Lie group roots, while the physics is exclusively looking at decompositions where different roots represent different things. What do you think about this chart at Theory_of_everything#Conventional_sequence_of_theories. Do you know where it comes from? It looks like SU(3)×SU(2)×U(1) belongs at the Electronuclear force level, from the Georgi–Glashow model? Anyway, if you can see definite places where diagrams are helpful, I'd be glad to work with you, to make diagrams or graphics. Tom Ruen (talk) 23:59, 22 January 2012 (UTC)

That, in general, seems like a nice plan. So, we have a few points to figure out. First, how do we distinguish fermions (fundamental representations), from bosons (adjoint representation)? I mean, a way that is clear to a reader. The point of decomposition is quite tricky. First, we would need to see a way to indicate symmetry breaking mechanism, and secondly, it would be important to understand how to deal with the 2D, 3D projections from higher dimensional spaces. The division you mention is just a way to commonly decompose theories. Historically, because we found that the strong, the weak and the em forces are easily quantized, then we tend to group them together in GUTs before we attempt to unify them with gravity. Within the standard model group, SU(3)×SU(2)×U(1), usually we assume that the two weaker forces, the e-m and the weak force, separate from SU(3) before they separate from each other. Ultimately the only local symmetry still unbroken (that we know of) is the SU(3)_c×U(1)_E-M. This decomposition, though, isn't necessarily the right one. Other theories in fact have different ways of breaking a larger group into the standard model group. Usually all these decompositions include some Higgs field acquiring some vev and spontaneously break the group symmetries. Other more complex methods sometimes break supersymmetries and trigger also some other symmetry breaking... but that's not really important here. ~GT~ (talk) 03:52, 23 January 2012 (UTC)

U(1)

This 3D diagram shows a plane linearly polarized wave propagating from left to right with the same wave equations where $\mathbf {E} =E_{0}\sin(-\omega t+\mathbf {k} \cdot \mathbf {r} )$ and $\mathbf {B} =B_{0}\sin(-\omega t+\mathbf {k} \cdot \mathbf {r} )$

I backed down to a question I finally could answer, namely what U(1) is doing in the EM theory, i.e. simple harmonic motion between electric and magnetic fields, so I remembered the diagram, of orthogonal light waves, and found one on wikipedia, but its wrong Light_wave#Electromagnetic_theory, missing the 90 degree phase shift: File:Light-wave.svg. I found a correct graphic at [2]. So I wonder we can expand the Theory_of_everything#Conventional_sequence_of_theories section with more graphic support, showing each unification step! So first step, fix the EM graph I guess! Tom Ruen (talk) 04:01, 25 January 2012 (UTC)

I'm not sure I understand. I see on that graph the same thing that I see in the one you pointed out. Maybe the perspective isn't awesome so it's not clear. But they both look like orthogonal to me. Or did you mean something else? ~GT~ (talk) 04:30, 25 January 2012 (UTC)

Okay, an animation too! But the issue is the waves are not just gometrically orthogonal, but they need a time phase shift of 90 degrees, like (x,y,t)=(cos(wt),sin(wt),t), but the equations on the capation are just sin() for both E and B? The [3] shows this phase shift between the yellow and blue waves. Am I wrong? I can't yet tell... Electromagnetic_wave_equation#Solutions_to_the_homogeneous_electromagnetic_wave_equation Tom Ruen (talk) 04:55, 25 January 2012 (UTC)

Back to my undergrad physics book, indeed (like wikiarticle), phases are together, and my intuition was wrong, thinking E-M waves were "rotating vector" magnitudes like potential and kinetic energy of a pendulum. Oh, where did I go wrong? .... Tom Ruen (talk) 05:15, 25 January 2012 (UTC)

Here's a website[4], someone saying the same as me, but maybe we're both just requiring something that isn't! A mystery to me. And another [5], with phase shifted animation [6]. That's what I'd expect! Tom Ruen (talk) 05:27, 25 January 2012 (UTC)

I think that guy's page is definitely some strange attempt of doing original research reverting some common knowledge about e-m waves. Of course I don't mean to say that whatever he says is necessarily stupid, since it's possible that a lot of the things he says are much more mathematically or physically subtle than what I see right now in a couple of minutes. Anyhow, at a very first look his tone is a give away to me. To be a little more serious about what he writes I think that his problem, which is what may also connect with what you are thinking, is that the energy of a wave must be the same at each time, which seems reasonable, but then he identifies 'each time' with each 'location in space', which seems to me to be the weak link. In fact, the front wave is what moves, and it's how the energy is actually carried. Then he starts with some random association with photons and how photons are related to a wave, and that also seems to me to show some sort of poor understanding (again, I might be wrong, maybe I'm being too fast and superficial). In facts, when you want to include photons, or any sort of quantistic version of E&M, then it makes no sense starting talking about E and B being in counter phase because the energy is supposed to be constant (or, I really don't see how that is related at all). If you want to use photons then, if anything, you should think of them as wave packets, that definitely don't carry constant energy along the propagation direction, by definition of a packet. But again, I don't think that page makes really too much sense. Does this help? ~GT~ (talk) 05:51, 25 January 2012 (UTC)

Thanks for your reading - I agree lots of potential confusion on the website animation, between time and spacial axes. I jumped to my similar "wrong" conclusion, seeing E-M as unified by the circle group, so I imagined two axes of the complex plane as E and M magnitudes! What's your interpretation - what does E-M unification via u(1) mean? What is conserved in this unification? Tom Ruen (talk) 00:32, 26 January 2012 (UTC)

Maxwell's equations#Ampère's law with Maxwell's correction says "Maxwell's correction to Ampère's law is particularly important: it shows that not only a changing magnetic field induces an electric field, but also a changing electric field induces a magnetic field. Therefore, these equations allow self-sustaining 'electromagnetic waves' to travel through empty space". This statement to me implies an oscillatory system, with energy moving between two forms as a function of time. So I just don't get how you can talk about E/B intensities being in phase like the sine equations above. Tom Ruen (talk) 07:48, 26 January 2012 (UTC)

I'm sorry I guess I had assumed a lot of things as given and hadn't realized what you meant with 'what U(1) is doing in the EM theory'. That U(1) has nothing to do with the two vectors E and B and the fact that they are orthogonal to each other and in phase (or not). That U(1) has to do with the fact that the theory is invariant under a gauge transformation. The sentence you reported is perfectly compatible with a wave function, which you shouldn't visualize as just an individual line with fields, but as the entire space filled up with those front planes carrying the EM wave. Also, self-sustaining waves don't imply at all energy moving back and forth from each other. To see how they influence each other just look at Maxwell's equation, because those are what's telling you how they react to each other. It might be useful to look at the relativistic classical EM formulated as gauge theory. ~GT~ (talk) 08:22, 26 January 2012 (UTC)

Your input is needed on the SOPA initiative

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