Braids, circulants, and Jordan algebras

Sheppeard brings together a number of correspondences and formal schemes in her attempt to recreate the standard model. Here I will touch on Sundance Bilson-Thompson’s braids, Carl Brannen’s circulant matrices, and Michael Rios’s Jordan algebras of observables for quantum gravity. In a nutshell, the fermions of a single generation are represented by braids, the circulants encode information about the generations, and the Jordan algebras associate the braids with the circulants.

In Bilson-Thompson’s braid correspondence, the fermions of a single standard model generation are represented by braidings of three “ribbons”. A ribbon may itself contain a twist; the electric charge of a braid containing m twists and n antitwists is (m-n)/3. The correspondence suggests a topological realization of the rishon model; but Bilson-Thompson’s correspondence still lacks a counterpart to the Harari-Seiberg hypercolor lagrangian. That is, no-one has put together a well-defined dynamical theory in which the braids interact as they should.

Carl Brannen is working on an algebraic preon model which seeks to explain the Koide mass formula. It turns out that masses satisfying the formula are eigenvalues of a 3×3 circulant matrix. Brannen and Sheppeard have worked on expressing all the standard model mass matrices in terms of circulants.

Finally, Michael Rios has written a series of papers in which he aspires to have M-theory emerge from a matrix model based on the exceptional Jordan algebra. Here he defines the algebra of observables in terms resembling loop quantum gravity; here he claims the result resembles an octonionic twistor string. Loop quantum gravity is the framework within which Bilson-Thompson’s correspondence is usually pursued, and it seems that Sheppeard hopes to motivate an association between braids and circulants via something like Rios’s constructions.

This effort has been going on since 2005 or so, and features in several of Sheppeard’s recent papers.

 

 

viXra:1201.0097 – “A Ribbon Dark Sector and Koide Triplets”

Sheppeard’s latest paper is very ambitious. It is a paper of many firsts. It is the first paper anyone has written that mentions Alejandro Rivero’s “new Koide tuple”, discovered in November 2011. It is the first paper which addresses and tries to explain Louise Riofrio’s observation that the dark energy fraction of the energy density of the universe is about three times the dark matter fraction. It appears to be the first paper extending Sundance Bilson-Thompson’s braid scheme for the standard model to the dark sector.

The paper undoubtedly looks strange by ordinary standards. There is no hint of a dynamical framework. Mathematically, it only contains simple algebraic formulas. There are leaps of logic and many peculiar statements. Combined with the general unfamiliarity of Koide tuples, Riofrio cosmology, and even Bilson-Thompson braids (which, despite having been the subject of a New Scientist cover story, are a fringe topic within theoretical physics), I think that most physicists, even if they somehow found themselves reading the paper, would quickly give up and put it aside.

I’ve had a few weeks to think about it, and for me, the jury is still out. The basic empirical facts – the various Koide relations, now extending to all the standard model fermions; Riofrio’s observations – are certainly worth thinking about. There is a 3:1 ratio appearing in both domains (Koide relations, dark sector fractions), and it is not beyond imagining that in both cases it is a manifestation of the 3:1 ratio of colored quark states versus colorless lepton states. It is even conceivable that the specific algebraic relations that Sheppeard proposes (qutrit path counts, sums of 2π/27 phases) are part of the explanation. But it is also very conceivable that they are not.

Introduction

This blog will serve to record occasional thoughts and observations about the work of the physicist Marni Sheppeard.