  SO(10), or equivalently its covering group Spin(10), is a well-known
promising grand unified group that contains the standard-model group. The
spinors of the group Spin($N$) of rotations in $N$ spacetime dimensions are
indexed by a bitcode with $[N/2]$ bits. Fermions in Spin(10) are described by
five bits $yzrgb$, consisting of two weak bits $y$ and $z$, and three colour
bits $r$, $g$, $b$. If a sixth bit $t$ is added, necessary to accommodate a
time dimension, then the enlarged Spin(11,1) algebra contains the
standard-model and Dirac algebras as commuting subalgebras, unifying the four
forces. The minimal symmetry breaking chain that breaks Spin(11,1) to the
standard model is unique, proceeding via the Pati-Salam group. The minimal
Higgs sector is similarly unique, consisting of the dimension~66 adjoint
representation of Spin(11,1); in effect, the scalar Higgs sector matches the
vector gauge sector. Although the unified algebra is that of Spin(11,1), the
persistence of the electroweak Higgs field after grand symmetry breaking
suggests that the gauge group before grand symmetry breaking is Spin(10,1), not
the full group Spin(11,1). The running of coupling parameters predicts that the
standard model should unify to the Pati-Salam group Spin(4)$_w
\times$Spin(6)$_c$ at $10^{12}\,$GeV, and thence to Spin(10,1) 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.

General Physics;High Energy Physics - Theory