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Quote of the Week

While this is a tragedy against womens’ rights, this is pretty normal stuff online. You should have seen what happened when I made the front page of Digg, back when people used Digg. Owwie. But I was okay with this, because I have a strong support network, and when I chose this path, I had a fairly clear idea of the consequences. I chose to be a semi-public figure.

I just didn’t expect the death threats.

Naomi Dunford

This is just ugly. What happened to respect for women?

ReplyDeleteI am not exactly sure where to put this question/comment,

ReplyDeletebut I have some sympathy for people such as Naomi who are subjected to unwarranted attacks,

so

I thought I would put it here even though it on the surface looks like a mostly-math question.

In my physics model I have a 3-state Higgs with mass states roughly around 140 GeV and 200 GeV and 240 GeV that is still in the game with respect to LHC results, particularly the results so far from the Golden Channel Higgs to ZZ to 4 leptons.

The states seem to me to be related to viewing the Higgs as a Tquark condensate.

Since my physics model is based on Clifford Algebra,

and the quarks are represented by half-spinors

which look like minimal left ideals of primitive idempotents

I am tending to think that the Higgs - quark relationship (Yukawa coupling)

might be explained by

considering the Higgs as primitive idempotent things

therefore naturally related to quarks as ideals.

In your blog some time ago you referred

to work of Carl Brannen on MUB's in relation to primitive idempotents

and

to arXiv 0710.5642 by Monique Combescure who said:

"... in prime dimension d = p , the Discrete Fourier Transform F together with a suitable circulant matrix C allow to construct a set of d+1 MUB's ..."

and

you said in a 2 March 2009 blog entry "... Consider the MUB matrices in prime dimensions p . If we demand that the entries form a finite field of p+1 elements (that is, including 0) it follows tht p must be a Mersenne prime ...".

The basic Clifford algebra structures in my model are related to the Mersenne primes:

3 = 4 - 1 of Cl(4) which Carl Brannen has described in a lot of explicit work

7 = 8 - 1 of Cl(8) whose 8-dim half-spinors look to me like 8 first-generation fundamental fermions

127 = 128 - 1 of Cl(128) = Cl(8)xCl(8)xCl(8)xCl(8)xCl(8)xCl(8)xCl(8)xCl(8)x

xCl(8)xCl(8)xCl(8)xCl(8)xCl(8)xCl(8)xCl(8)xCl(8)

(from 8-periodicity and 128 = 8x16) (physically explaining

the large size of the Planck mass squared

whose inverse gives the apparent weakness of gravity)

Since the Higgs in my model should be represented by the primitive idempotents

of the Cl(8) in terms of which quarks are represented as half-spinors

I would like to get a better understanding of the explicit detailed

structure of the Cl(8) primitive idempotents.

As of now, my visualization is roughly that the idempotents

live in these part of Cl(8) graded structure:

1 pseudoscalar

6 of the 70 middle grade-4

1 scalar

Maybe if I had better understanding of the corresponding MUB's for Cl(8)

and their related structures (circulants, Discrete Fourier Transforms, etc)

I would have a deeper understanding of how Higgs works

(and why you say that you do not believe in Fairy Fields as Fundamental).

Do you have any papers or references to stuff by others that

have detailed explicit descriptions for the Cl(8) case ?

Tony

PS - I apologize if I put this in the wrong place or

if it is too long and complex for a blog comment,

so feel free to delete it if you think it should be deleted.

Good question, Tony. I am not sure that what you want exists as yet, but the Combescure papers are a good place to start, since she covers MUBs in all dimensions $p^k$ (ie. you should just start with the MUBs for the right dimension). I see a few recent things along those lines.

ReplyDeleteOr this.

ReplyDeleteThanks very much for the references to the Caltech thesis of Prabha Mandayam Doddamane and the arXiv paper 1004.5086 by Prabha Mandayam, Stephanie Wehner, and Niranjan Balachandran.

ReplyDeletearXiv 1004.4086 said:

"... we construct special sets of up to 2n+1 mutually unbiased bases (MUBs) in dimension 2^n which have particularly beautiful symmetry properties derived from the Clifford algebra ... there exists a unitary transformatin tht cyclically permutes such bases. This unitary can be understood as a generalization of the Fourier transform, which exchanges two MUBs ...".

If I look at the case n = 3,

that gives me 7 MUBs in Cl(2^3) = Cl(8)

and the 7 corresponds to the 7 pure half-spinors

which correspond to the 7 fermion particles with tree-level mass

(in my model the 8th fermion, neutrino, gets mass by corrections beyond tree level).

arXiv 1004.4086 and the Caltech thesis said:

"... for L = 8 classes in dimension d = 16, no partitioning for operators can be found satisfying our requirements ...".

I need to understand that because Cl(16) = Cl(8)xCl(8) is the natural home of E8 = bivectors of Cl(16) + half-spinor of Cl(16)

and of course E8 is a basic part of my E8 physics model.

In that regard,

Appendix B of the Caltech thesis "Constructing Maximally Commuting Classes of Clifford Generators" is something that I need to study and try to understand.

Something else that I need to work to try to understand is the relationship between Entropic Uncertainty Relations (EURs) and MUBs, so I have a lot of work to do while I wait for the end of this LHC run around Halloween.

Maybe my work-space can be regarded as a pumpkin patch that is sincere enough that the Great Pumpkin will bring happy LHC results.

Tony

PS - It probably was good for me to post this comment on this entry,

because

Prabha Mandayam Doddamane, the Caltech thesis and primary arXiv author,

is indeed female (as is Stephanie Wehner)

and

her work speaks for itself with a voice that is far louder

than

any voice of any anti-female attacker.

That's great, Tony. If you convince yourself of the non existence of fairies via this route, please let us know, although ultimately I believe this is a matter of principle, that the LHC will soon decide.

ReplyDeleteI have convinced myself of the non-existence of

ReplyDeletethe Standard Model Higgs as a fundamental particle

by

identifying it with part of the Primitive Idempotents

of the Cl(8) real Clifford algebra (equivalent to MUBs I think).

Instead of a simple-minded fundamental scalar particle,

the Higgs is seen as a quantum process that creates a fermionic condensate with which it interacts to make the fermions appear massive.

When I work through the details using my E8 physics model

as a sort of template,

I see that the Primitive Idempotent Higgs does all the nice

things that the fundamental scalar particle Higgs need to do,

and

that effectively it looks like a Higgs-Tquark system

with 3 mass states (i.e., the LHC should see events that

look like 3 standard model Higgs mass states

at around 140 GeV and 200 GeV and 250 GeV

with the total standard model cross section

being divided up among those three states.

In particular, the LHC should see a Higgs around 140 GeV

but with a lower cross section than expected.)

I have written up a 2-page pdf description of the

Higgs as Primitive Idempotent idea and put it on the web at

tony5m17h.net/PrimIdemE8hTq.pdf

Any thoughts, comments, and criticisms would be much appreciated.

Tony

Thanks, Tony.

ReplyDeleteTony, as always, I think your prediction is first class, since it fits the right framework for EW symmetry breaking. I will certainly be cheering if you are correct.

ReplyDeleteBut as usual, I think this (correct) mechanism requires a rethinking of the concept of particle, so that categorical braids and operads are more fundamental even than Clifford algebras etc. That leaves the question of what happens to your triplet of mass states in the more abstract setting, and that comes down to the nonlocality in my views on cosmology. FourierSusy should provide a bosonic dual to your fermionic condensate, but can this be observed (locally) at the LHC at your mass values? I don't believe so. This then really is the key to the matter, is it not? To be or not to be? Anyway, your bet is way ahead of the stringers and loopies!

As to bosonic dual to fermionic condensate

ReplyDelete(i.e. looking at the 4+4 = 8 parts of the Cl(8) Primitive Idempotent

in terms of creation/annihilation operators of 8 = 4+4 -dim spacetime)

that seems to lead to spacetime as a bosonic condensate

based on Conformal Gravity which would involve energy levels

near the Planck scale and therefore beyond the reach of the LHC.

As to how Braid models compare to Clifford Algebra models:

The most recent paper about Braids that I have seen is

arXiv 1109.0080 by Bilson-Thompson, Hackett, Kauffman, and Wan.

They said:

"... the Bilson-Thompson ... Helon model ... is based on the preon model of Harari and Shupe

...

braided states in the trivalent scheme ... would allow particle propagation, but not interactions ...

[so]... a 4-valent scheme ... as tubular links between spherical nodes ... was developed ...[which]... gives rise to forms of braid propagation and interaction that are analagous to the dynamics of particles

...

Given any framed trivalent network, we can always combine adjacent nodes to create composite tetravalent nodes. Likewise, the tetravalent nodes obtained by ... slicing a tubular link down opposite sides ... can be decomposed into pairs of trivalent nodes. ... We thereby obtain a model which allows us to reproduce both kinematic and dynamical aspects of the Standard Model.

...

charge ...[is]... mapped to the braid's effective twists

...

how mass arises? ... a braid may acquire zero or nonzero mass from some of its intrinsic attributes. ... the number of crossings can be a candidate for its mass ...[so]... all actively interacting braids seem massless, consistent with their analogue with (gauge) bosons ...

[alternatively] mass ... is emergent in the low energy limit

...

three strands of a braid may ... be attached to nodes far from each other on the network causing the braid nonlocal

...

a theory that naturally gives rise to our (3+1) spacetime is still missing ...".

With respect to Clifford Algebras:

The 8-dim Clifford Algebra Cl(3) has graded structure 1+3+3+1

that corresponds directly to the Harari-Shupe structure

and

therefore also corresponds directly to the Helon Braid structure.

Since the Clifford algebra Cl(8) can be seen as

a nested Clifford algebra Cl(Cl(3))

the nice Braid structure is also present in Cl(8) and

therefore also in the E8 Physics model.

In the E8 Physics model particle masses are calculated using the geometry of bounded complex domains related to the Standard Model symmetry groups,

which seems to me to be consistent with the alternative "emergent in the low energy limit" picture of arXiv 1109.0080.

Tony