A strange theory of everything: dust on [itex]\mathbb{R}^{0|18}[/itex]

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https://arxiv.org/abs/0805.3819
Approximating the Standard Model and gravity with dust on [itex]\mathbb{R}^{0|18}[/itex]
Robert N. C. Pfeifer
[Submitted on 25 May 2008 (v1), last revised 11 Jul 2020 (this version, v14)]
This article describes a single species of non-interacting massless dust on [itex]\mathbb{R}^{0|18}[/itex], whose behaviour in the low-energy limit is equivalent to an interacting family of massive particles resembling the Standard Model plus WIMPs on a curved 3+1D space--time manifold (though with some liberties taken with gravity). The coupling between mass and curvature is not strictly equivalent to general relativity, but reproduces the usual metrics for large uncharged spherically symmetric sources at reasonable distances from the event horizon. Tunable parameters may be chosen so that electroweak particle masses and force couplings calculated to tree level lie within a few percent of their Standard Model values. This model is consequently of interest as a novel approximation to the Standard Model and gravitation. Extensive new physics, including a tripartite coloured preon substructure for fermions, is predicted at energies beyond the strong nuclear scale.

https://arxiv.org/abs/2008.05893
Particle generations in [itex]\mathbb{R}^{0|18}[/itex] dust gravity
Robert N. C. Pfeifer
[Submitted on 11 Jul 2020]
The [itex]\mathbb{R}^{0|18}[/itex] dust gravity model contains analogues to the particle spectrum and interactions of the Standard Model and gravity, but with only four tunable parameters. As the structure of this model is highly constrained, predictive relationships between its counterparts to the constants of the Standard Model may be obtained. In this paper, the model values for the masses of the tau, the W and Z bosons, and a Higgs-like scalar boson are calculated as functions of [itex]α[/itex], [itex]m_e[/itex], and [itex]m_μ[/itex], with no free fitting parameters. They are shown to be 1776.867(1) [itex]MeV/c^2[/itex], 80.3786(3) [itex]GeV/c^2[/itex], 91.1877(4) [itex]GeV/c^2[/itex], and 125.16(1) [itex]GeV/c^2[/itex] respectively, all within 0.5σ or better of the corresponding observed values of 1776.86(12) [itex]MeV/c^2[/itex], 80.379(12) [itex]GeV/c^2[/itex], 91.1876(21) [itex]GeV/c^2[/itex], and 125.10(14) [itex]GeV/c^2[/itex]. This result suggests the existence of a unifying relationship between lepton generations and the electroweak mass scale, which is proposed to arise from preon interactions mediated by the strong nuclear force.

These papers are rather odd, but there are two things I would like to understand.

First is the use of [itex]\mathbb{R}^{0|18}[/itex]. For those unfamiliar with the notation, the object [itex]{M}^{m|n}[/itex] is a "supermanifold" with m bosonic dimensions and n fermionic dimensions. Bosonic dimensions are real-valued like familiar space and time, but fermionic dimensions are measured in anticommuting "Grassmann numbers". That the author's starting point is dust in a space with no bosonic dimensions and 18 fermionic dimensions would already make this worth a second look, just to see how that worked.

Then he goes on to claim successful derivations of a number of standard model parameters. And looking into the second paper, I see he uses a matrix with (in his words) "a strong resemblance to Koide's K matrix for leptons". So that's the second thing to understand - just what his variation on Koide is, and how it is related to that purely fermionic supermanifold that he starts with.
 
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Answers and Replies

  • #2
ohwilleke
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Worth a closer look despite the fact that it does indeed seem rather odd.
 
  • #4
ohwilleke
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It doesn't look like this particular paper was ever published, although many other papers by the same author are widely cited, however, so it doesn't look like a crackpot paper. It looks like the author has moved on to less ambitious papers in a somewhat different speciality in recent years. https://scholar.google.com/citations?user=D9oCceYAAAAJ&hl=en&oi=sra

A footnote to the paper suggests a reason for the shift:

"While the majority of this work was performed at the Perimeter Institute, significant portions also took place at (in chronological order) The University of Western Australia, The University of Queensland (Australia), and Macquarie University (Australia)."
 
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A few more words on how this theory is supposed to work... The key intermediate construct, between the starting point ("dust" on a timeless supermanifold of 18 complex Grassmann dimensions), and the standard model, is a 4-dimensional SU(3)xSU(3) gauge theory acting on a large multiplet of fermionic preons.

A four-dimensional space-time arises by picking out two of the complex Grassmann coordinates. It's a submanifold of the original supermanifold. And the gauge freedom has something to do with changes of coordinates in the original supermanifold... the SU(3)s are subgroups of a GL(9) symmetry there. The preons, meanwhile, are quasiparticles built from the dust field, which is postulated to be in a disordered quantum state (in the sense of condensed matter).

Finally, the lepton mass ansatz comes from Koide 2000, in which Koide introduced a circulant ansatz. In Pfeifer's theory, the leptons are made of three colored preons (he seems uncertain as to whether this is QCD color, or something deeper), and the preons acquire mass by interacting with modes of the gauge field. The Koide circulant ansatz is said to approximate this.
 
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