Article: An exceptionally simple theory of everything
References:
- A Geometric Theory of Everything, December 2010, Scientific American
- Elementary Particle Explorer
| File:Gta-1.png 1 |
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| File:Gta-4.png 4 |
File:Gta-5.png 5 |
File:Gta-6.png 6 |
| File:Gta-7.png 7 |
File:Gta-8.png 8 |
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MOVED Comments by ~GT~
editAbout the figures linked above, as I said above, I think they are nice pictures and should be used more often. But they also have some bad consequences, as in people not really understanding how two GUTs differ from each other, or what's the difference between roots and weights, or what's the difference between bosons and fermions in those diagrams. Anyhow these are just opinions. Instead, calling the pictures by numbers n), the facts are: [For 9 diagrams at [1]]
1) This is a correct picture. I usually don't like to see antiparticles in these diagrams but that's OK (and a long discussion). The Higgs is a little strange. Where is the h+ degree of freedom that usually is used to be eaten by the W bosons to get their masses (actually were are the 3 degrees of freedom eaten)? I.e., from this diagram I don't see the Higgs as a 4 or natural bidoublet in SU(2)_LxSU(2)_RxU(1)_X. For the same reasons maybe the SU(2)_R patterns maybe don't show? But then I would have expected to see at least the other 3 higgs degrees of freedom given that there is no symmetry breaking yet. Am I misunderstanding something or did I get confused?
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.
3) Although I like this picture, and I know what it means, I doubt that people understand it easily. Understanding 4 dimensional spaces projected onto 2 isn't intuitive. They will just *see* a charming pattern (that I can create with any orthogonal two dimensional spaces). Also, the caption/comment below the picture is misleading, if not even false. That's absolutely not the Standard Model. That is the representation of the standard model gauge bosons and some fermions, certainly not the entire standard model (since some of the fermions, which are a fundamental property of the standard model) are missing in that picture.
4) This is OK if the previous points were clear (it doesn't add more problems to the ones already mentioned). I like the idea of showing SU(5) and it's fundamental representation, but I think that the projection can be confusing.
5) I am not sure that every quantum number of E6 is accounted for, using only the known particles with the conventional quantum numbers (I don't want to check, and I shouldn't be checking anyways, but I can if needed), and the same issue regarding the 3 generation problem stands here.
The ones after 5) all share the same problems as the ones above, plus the fact that it's not obvious from the captions that the E8 one doesn't actually fit the standard model because of the 3 generation problem. It is phrased in a very cryptic way that hides the issue.
Overall I believe that the papers cited certainly prove that not only physicists know those diagrams and patterns (even with the strong force, or color), but also that when they need it they actually use it. In most cases they don't need it because physicists understand the representations well enough just from the math without making pictures, but in that specific case a picture was explicitly used because it is not easy to visualize G2 and it's *analogy* with SU(3) plus 3 and 3bar, unless you see the graph. I agree that Lisi's representations are interesting, although I think he fails to show how lots of other theories have the same patterns.
I think that the statement reported from SciAm "Even if Lisi turns out to be wrong, the E8 theory he has pioneered showcases striking patterns in particle physics that any unified theory will need to explain" is simply journalistic, but not accurate nor true. In fact, Lisi's theory certainly wasn't the first theory to identify those patterns. And the diagrams in the papers I linked certainly are the proof of him not being the first to notice this patterns. The patterns were certainly noted a long time ago, when the first GUTs were studied (that's the whole point of having a GUT!). The SU(5) example that Lisi has drawn is the proof that people knew already about the patterns when designing SU(5) and noticing how well it fit with the known particles. And all the SU(3) famous flavor diagrams, and the diagrams included in the papers I mentioned above (plus all the examples made to students in grad schools) are the proof that they aren't original.
Now, it is true, using these patterns Lisi made a clear and important impact on viewers and curious people. Actually I think that a lot of people got charmed by his theory by looking at his diagrams (and they didn't realize how common some of these patterns are). Maybe more physicists should use them. And maybe there should be more work trying to explain them and their projections. And maybe in the future we could write a sentence along these lines: "in presenting his theories to the general audience, Lisi introduced to non-physicists the weight diagrams to look at patterns not only in quark/meson/baryon structures, but also in fundamental particles and unification. The Standard Model seen as a weight diagram offers to non experts a better visualization of all the striking patterns of the Standard Model than the usual table of particles and charges" (which is what I believe, honestly). And I hope that in the future this becomes a recognized fact, but I don't think there is any consensus and reliable sources that are accurate and state so about Lisi at the moment. ~GT~ as98.244.54.152 (talk) 04:52, 7 January 2012 (UTC)