My approach to elementary particles is to try to build them up from a Clifford algebra assumed to have something to do with spacetime. This is inherently geometric, but it is not the only way to do geometry. A similarity is that both of us end up relating the three spatial dimensions to color. (Forgive me if I read too much into your papers, Jay.)

I keep finding similarities with what Jay R. Yablon is doing. While my approach is algebraic, he uses tensors. Unlike the usual approach to elementary particles, he puts tensors at the root and more or less derives the symmetries from there. For example, with the elementary particles, he gets that the 4x3x2 structure of the fermions arises from the 4! = 4x3x2x1 permutations of the four spacetime indices. From his recent paper, the fermions are organized as follows (with L=leptons, R, G, B = colors of quarks):

As I do, Jay relates the structure of the baryons to the structure of quarks. Further, he goes into looking at the hydrogen atom as a composition of three quarks and a lepton. This is fun stuff.

Interesting? Go visit Jay’s obscure blog and read the tensor theory behind all this.

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Hi Carl,

I’ll add a brief comment now, then expand later both here and at http://jayryablon.wordpress.com/.

You say “both of us end up relating the three spatial dimensions to color.” Actually, not exactly, but close. Because a baryon is a third-rank antisymmetric tensor (in my view, details on my blog, above, and web site http://home.nycap.rr.com/jry/FermionMass.htm), and because each of the three spacetime indexes gives rise to one of the three fermions which constitute the baryon, the “three” colors arise not from three spatial dimensions, but from three spacetime indexes on the baryon density. And, *very importantly*, they arise from the exclusion principal which is very vital and central to the entire paper which you have been so kind as to reference here.

All else is accurate and I am glad you zoned in on Figure 3 and reproduced it here. In fact, while away this weekend, I decided to come back and extract Figure 3 separately, only to find you had done so already.

So, not only are there similarities in what we are doing, we seem to be thinking alike. Great minds? Or . . .? ðŸ˜‰

Best,

Jay.

OK, nice paper, although I prefer a higher level of abstraction when discussing spacetime. I especially liked the collapsing hexagon Feynman diagram – sounds familiar!

Hi Carl,

You are a student of Clifford Algebras. I saw your reply to Martin Bauer, then posted my own at:

http://jayryablon.wordpress.com/2008/02/06/lab-note-2-part-2-gravitational-and-inertial-mass-and-electrodynamics-as-geometry-in-5-dimensional-spacetime/#comment-1311

Can you take a look at this and let mw know if you concur that this is a valid way to create projection operators, and if you concur that the chirality problem arises from attempts to make the fifth dimension spacelike rather than timelike. Note: with the extra time dimension, one has the two degrees of freedom in time which you refer to.

Jay.

Hi Marni:

Glad you enjoyed the paper. I tend to prefer concreteness myself when we talk about spacetime, because we have only one physical universe and ought to know which specific choice from among many permitted by abstractions, is the one chosen by nature.

Would like your thoughts on the validity of applying the collapsing hexagon to baryons in the manner shown.

Took a brief look around http://kea-monad.blogspot.com/ and am adding you to my blogroll.

Best,

Jay.

Of course I thought the application to the baryons was interesting, but I’m really not sure whether or not it is correct. I agree that confinement is linked to spatial dimension with the use of hexagons in category theory, but I have been working on the (perhaps false) assumption that small black holes (‘spacetime structure’) will be easier to understand than baryons, which I have been thinking of in terms of ‘composites of composites’. Unfortunately, I make things difficult for myself by avoiding as much as possible the task of organising the particles, until I feel I understand the mechanisms better.

. . . because we have only one physical universe and ought to know which specific choice from among many permitted by abstractions, is the one chosen by nature.I disagree. There isn’t “one physical” universe. Physical = Newtonian. Also, consider that nature allows, for instance, commutative and non-commutative math.

Pioneer1: Why do you say “Physical = Newtonian”? That seems to read an awful lot into Newtonian or an awful little into physics.

Hi Carl, Getting back to physics after about two years off. The link to my paper in this post went bad, so I fixed it over in my blog. Yoy may wish to spiff up your links accordingly. Best, Jay