Arcadian Pseudofunctor: Theory Update 100

Wednesday, August 10, 2011

Theory Update 100

e_{8}

algebra is clearly about qubits and qutrits. One considers the qubit cube

Z_{2}^{5}

, corresponding to the field

F_{32}

with

32

elements. This sits inside the

2 \times 2

matrix group

S L (2, F_{32})

, conveniently in the form

which is used for braids in emergent geometry. A

32

dimensional information space could be a plane over the bioctonions. Triality also appears, because

248 = 192 + 56

.

7 comments:

KeaAugust 10, 2011 at 4:47 PM
And recall that the oft appearing number $288 = 2^{5} 3^{2}$ satisfies $1 / 288 = 0.0035$ . This is a parameter in the (triality respecting) form of the CKM quark mixing matrix. The other $2$ parameters are $24$ and $- 0.231$ .
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KeaAugust 10, 2011 at 5:13 PM
And remember that there are three nice ways to place a $2 \times 2$ matrix inside a $3 \times 3$ one, as in the tripling of spin for the generation quantum number, resulting in the Koide relations for particle masses.
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Daniel de França MTd2August 11, 2011 at 3:15 AM
Marni, the link you provided to Konstant is also about John Baez talking about Garrett's e8. But his model has lots of higg's fairy fields, as you call them. Isn't that a bad thing?
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KeaAugust 11, 2011 at 11:34 AM
Daniel, if you read two paragraphs of one of my papers, you would know that I have never, in any way or form, advocated a Lisi model. Lisi did not invent the Lie group $E_{8}$ . Read the Kostant paper.
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KeaAugust 11, 2011 at 4:19 PM
By which I mean to say, mathematics is one thing and physics is another thing entirely. As kneemo has often pointed out, we need a $57$ dimensional picture for $E_{8}$ (in its Jordan algebra guise). This can be $57 = 56 + 1$ , but observe that we also have $57 - 3 = 54$ with $54$ the $C O$ dimension, and the $54$ can be split into three lots of $18$ so that there is a nice $3 \times 3$ packaging for the $57$ dimensions.

Oops, must correct the post then. Done.
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L. Edgar OttoAugust 12, 2011 at 8:59 AM
Kea,

In case you have not seen it my new graphs have reached many of the same number relations although I don't see how people do it without a picture.

In retrospect the idea of mass and fairy fields and SUSY seem a small part of the concepts- not to those bloggers with sensible imaginations. I like to count the empty spaces also.

The PeSla
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KeaAugust 12, 2011 at 9:34 AM
Yes, ThePeSla, one should always aim for a viewpoint from which everything one was taught at school is but a small mound in the landscape below.
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