All fields of the standard model and gravity are unified as an E8 principal bundle connection. A non-compact real form of the E8 Lie algebra has G2 and F4 subalgebras which break down to strong su(3), electroweak su(2) x u(1), gravitational so(3,1), the frame-Higgs, and three generations of fermions related by triality. The interactions and dynamics of these 1-form and Grassmann valued parts of an E8 superconnection are described by the curvature and action over a four dimensional base manifold.
PDF of the paper
Daily Telegraph writeup
I like symmetries :-)
Update: QuickTime movie of E8 rotation in 8 dimensions, useful for identifying interactions between particle families
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simon
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Exceptionally Simple Theory of Everything
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Simon - 17:08 15/11/07
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Re: Exceptionally Simple Theory of Everything
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Simon - 10:37 16/11/07
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This is why I think it's so cool (from Garrett's explanation on BackReaction)
Choose any of the diagrams in the paper, draw a vector from the center of the diagram (the origin) to one of the particles, then draw another vector from the origin to a different particle. Add these two vectors (SGB: move the base of one vector from the origin to the non-origin end of the other while keeping its orientation the same), and see if the result lands on a third particle -- if it does, that's the result of the interaction.
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simon
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Deleted User Account - 13:22 16/11/07
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Re: Exceptionally Simple Theory of Everything
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Simon - 13:40 16/11/07
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On his own site, he rues the notion that he's going to be immortalised for the words "Holy Crap!" :-)
I've just listened to his talk from Tuesday's International Loop Quantum Gravity Seminar (you'll need the second PDF to follow all the slides) and while I can't pretend to understand a scintilla of the technical detail, I can just about follow along and work out what equation terms are relating to which standard model (and other) fields and particle families.
This is conceptual algebra and geometry at its finest!
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simon
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Re: Exceptionally Simple Theory of Everything
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Simon - 13:52 16/11/07
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Plus, it gives the opportunity to people to use phrases like this in complete seriousness:
four dimensional spacetime vs 11 dimensional spacetime with Kaluza-Klein orbifold compactifications
http://www.math.columbia.edu/~woit/wordpress/?p=617
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simon
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Re: Exceptionally Simple Theory of Everything
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David Crowson - 13:56 16/11/07
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"For its action on spinors, gravity is best described using the spacetime Clifford algebra,
C l(3, 1) — a Lie algebra with a symmetric product. The four orthonormal Clifford vector
generators,
γ1 = σ2
⊗ σ1 γ2 = σ2 ⊗ σ2 γ3 = σ2 ⊗ σ3 γ4 = iσ1 ⊗ 1
are written here as (4
× 4) Dirac matrices in a chiral representation, built using the Kronecker
product of Pauli matrices"
I may have to break google with all this looking up of terms :)
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bombholio
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Re: Exceptionally Simple Theory of Everything
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Simon - 14:05 16/11/07
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Try this - it's pretty good:
http://science.slashdot.org/comments.pl?sid=362251&threshold=1&commentsort=0&mode=thread&cid=21373093
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simon
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Re: Exceptionally Simple Theory of Everything
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Hugo van der Sanden - 04:34 18/11/07
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Try this one: week 106 of John Baez's "this week's finds in mathematical physics".
Hugo
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Re: Exceptionally Simple Theory of Everything
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Steve - 11:22 18/11/07
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That still splits my eyeballs.
Math just isn't my thing. Theoretical physics even less. I was really bad at math at school and I ended up having to take my math O-Level twice and I just scraped through on the second try.
But this stuff seems to fascinating that I wish I could understand it better.
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stevepa
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Deleted User Account - 20:56 18/11/07
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Re: Exceptionally Simple Theory of Everything
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Simon - 10:21 19/11/07
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exploration of altering the Phrygian modes
Won't take too long, surely?
Mode 1): Door Shut. Light Off.
Mode 2): Door Open. Light On.
... unless you want to invoke Schrodinger.
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simon
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Deleted User Account - 13:27 19/11/07
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Re: Exceptionally Simple Theory of Everything
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Bruce Ure - 13:29 19/11/07
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Yes but you can never be sure if they're going to turn up until you get there.
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