However, she is back as a blogger, and it’s impossible to ignore that, alongside posts about her work, there’s a steady stream of paranoid claims of persecution. I don’t know if it’s earnest, if it’s theater, if it’s outright hallucination due to extreme stress. But I’m pretty sure that it won’t help her return to an academic setting. So, in the hope that she can survive this too, a few comments from me, for the general reader.

First, denial of credit for one’s work, and radical alienation from one’s peers, can happen even to the most accomplished mathematicians and physicists. For the first, see the posthumous recognition achieved by Ernst Stueckelberg; for the second, see the later years of Alexander Grothendieck. Those are extreme cases, but there are many lesser cases too.

Second, I would say Sheppeard really has been ahead of her time, in *at least* the following ways. First, her minimal approach to beyond-standard-model physics. Second, her recognition that Koide, and Brannen, are onto something (and she’s still way ahead there). Third, her use of twistor polytopes, which are indeed central to progress now being made in quantum field theory. And probably fourth, simple quantum explanations for the dark sector.

Finally, it’s not just that people’s work can go unrecognized. Plagiarism and ostracism are very real phenomena, and their negative consequences can accumulate with time.

]]>I don’t have much to say about the cosmological ideas at this point. They belong to the genre of theory that would explain the dark sector through quantum effects on an astronomical scale. As for the details, in the past I have expressed doubts, but when facing the unknown, you have to start somewhere.

]]>She is aiming at a theory in which physics is standard model all the way up to the quantum gravity scale, and in which quantities like the mass matrices of the standard model are ultimately determined by what happens at that high scale. Various generalized Koide relations among fermion masses are the big clue we have about the details of that.

So here she begins with a model of neutrino mixing from noncommutative geometry (reference 1) – to be amended so that the deformation parameter θ appears directly as a mixing angle. In conventional terms we could say that this is an effective theory.

Then we have some algebraic speculations about where the Koide relations come from. For example, that the Brannen-Koide angle for the down quarks, of 4/27 radians (see page 17 of Sheppeard 2010), derives from the 2/9 radians angle for the charged leptons, acted on by a triality transformation of the exceptional Jordan algebra, which should play a role in quantum gravity.

To place this in context again, I think it helps to remember some of her other ideas – that Bilson-Thompson’s mapping of braids to standard-model fermions applies in some categorical way (in which braids are morphisms), that the dark sector is made of mirror braids and that mass originates in a kind of cohomological inner product of braids and their mirrors.

For the neutrino masses, she uses a Koide-like ansatz due to Brannen (a modification of his own rewrite of the original Koide formula), then changes a sign to get mirror neutrino masses, and claims a connection with the (current!) CMB temperature. To make sense, that last step is going to require some seriously nonstandard cosmology.

So, when it comes to specifics, there are a lot of details and I am not on board with most of them. But the criticality of the electroweak vacuum suggests that it really might be standard model all the way to the Planck scale, so the overall concept of getting Koide numerology from quantum gravity is a logical one. And a pioneering concrete proposal tends to inspire the construction of others.

]]>So spare a thought for Marni Sheppeard, who truly suffered for many years, waiting on tables while she did a PhD on twistor polytopes in a country at the very edge of the global physics map, who blogged openly about her ideas and was excoriated as a crackpot for her efforts, who starved herself in order to keep working on physics – and who now has to live with the spectacle of this media celebration, in which already well-paid and well-connected physicists dwelling in the elite institutions of the northern hemisphere are feted for their discoveries, while she remains as unknown and vulnerable as ever, and required to keep enduring whatever grim circumstances she is currently dwelling in.

There are many examples of people who were ahead of their time; who only got belated credit or no credit at all for their work; who anticipated a big discovery, either in a broad way or a highly specific way. The phenomenon comes in many forms. In this instance, here are some of the questions I would like to see answered: What is the relationship between Sheppeard’s body of work, and the new twistor physics now in the headlines? Is there anything that the twistor researchers with salaries and academic appointments can learn from the work that Sheppeard has managed to produce? And, is it still possible to get her into a position where she can work properly, make further contributions, and communicate with her peers?

I still do not know how to turn on comments for older posts, but hopefully the comment section for this one is open and working.

]]>But I could never quite grasp the logic whereby the density fractions were being predicted, and that was the big empirical claim to success. I also thought I saw a similarity to the Milne universe, but again, I never quite got it clear in my own head.

Much later I came to understand that the model was empirically problematic, because dark matter and dark energy density fractions evolve with time, so any numerology based on present-day observations is just picking out one moment in the history of the universe. It remains possible that the present-day values are special, e.g. perhaps they are the asymptotic values. One should also bear in mind that for Sheppeard, Riofrio’s handful of equations are a classical ansatz to be derived from a theory of quantum gravity.

The Planck satellite has in any case given us new values for the density fractions, that are no longer close to Riofrio’s numbers, so it’s an open question as to whether Riofrio’s ideas are still part of Sheppeard’s thinking. However, Sheppeard continues to champion another item of astrophysical numerology, which I believe was co-discovered by her collaborator Graham Dungworth – that the temperature of the cosmic microwave background equals the rest mass of a certain “mirror neutrino”, as predicted by a version of Brannen’s formula for Koide mass triplets.

This would be even more “problematic” than Riofrio’s numbers. The CMB temperature varies with the expansion, but that’s not fatal to the idea; quintessence models show that it’s possible to have mirror neutrino masses evolving with the size of the universe. The real difficulty lies in explaining the connection between CMB photons and mirror neutrinos at the level of particle physics and cosmic history.

One normally supposes that the CMB photons are simply photons which decoupled from the primordial plasma, once it had thinned out enough for neutral atoms to form, and which, ever since that time, have been travelling without scattering again. Neutrinos, mirror or otherwise, feature nowhere in this story, and yet they ought to, if the posited relationship is supposed to be real. Either the mirror neutrino ought to play a role in photon decoupling, or a completely different origin must be ascribed to the CMB photons, one with room for the mirror neutrinos to play a role. (Or the connection is spurious, which is what I think; but the ideas are still interesting to play with.)

]]>Chapters 2 through 5 are spent defining many simple combinatorial objects in the not-so-simple language of category theory. There are numbers, sets, trees, braids, polytopes, and matrices, among other objects.

In chapter 6, we make contact with current applications of twistors to quantum field theory. This is already an area in which combinatorial objects and simple symbolic calculi are playing a role, and Sheppeard wants to interpret the subject using concepts and results introduced in the preceding chapters.

In chapter 7, some of this apparatus is employed to introduce an extended version of Bilson-Thompson’s correspondence (of braids and Standard Model particles) and an explanation of Koide formulae in terms of circulant matrices associated with the braids.

So to summarize, chapter 6 is about the frontier of current theory and chapter 7 is about phenomenology, and in both cases there is an attempt to make the categorical combinatorics of chapters 2 through 5 relevant.

Chapters 8 and 9 return to pure math – knots, polytopes, and categorical diagrams.

Chapter 10 is about black holes – the “black hole / qubit correspondence” – and chapter 11 is about cosmology – the dark sector and cosmic time.

]]>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.

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