Six Bits

TL;DR

This paper proposes a unification framework using Spin(11,1) geometric algebra, incorporating standard model fermions with a six-bit code, predicting symmetry-breaking scales, and linking Higgs fields to cosmological inflation and neutrino masses.

Contribution

It introduces a novel six-bit coding scheme for spinors, unifies the standard model and Dirac algebra within Spin(11,1), and predicts specific symmetry-breaking pathways and cosmological implications.

Findings

Unifies standard model and Dirac algebra within Spin(11,1).

Predicts symmetry-breaking at $10^{12}$ and $10^{15}$ GeV.

Links Higgs fields to inflation and neutrino mass generation.

Abstract

The spinors of the group Spin($N$) of rotations in $N$ spacetime dimensions are indexed by a bitcode with [$N$/2] bits. A well-known promising grand unified group that contains the standard-model group is Spin(10). Fermions in the standard model are described by five bits $yzrgb$, consisting of two weak bits $y$ and $z$, and three color bits $r$, $g$, $b$. If a sixth bit $t$ is added, necessary to accommodate a time dimension, then the enlarged Spin(11,1) geometric algebra contains the standard model and Dirac algebras as commuting subalgebras, unifying the four forces of Nature. There is a unique minimal symmetry-breaking chain and associated multiplet of Higgs fields that breaks Spin(11,1) to the standard model. Unification to the Pati-Salam group Spin(4)$_w {\times}$ Spin(6)$_c$ is predicted at $10^{12}\,$GeV, and grand unification at $10^{15}\,$GeV. The grand Higgs field breaks $t$-symmetry, can drive cosmological inflation, and generates a large Majorana mass for the right-handed neutrino by flipping its $t$-bit. The electroweak Higgs field breaks $y$-symmetry, and generates masses for fermions by flipping their $y$-bit.