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**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.