Unification of the Four Forces in the Spin (11,1) Geometric Algebra

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 $durgb$, consisting of two weak bits $d$ and $u$, 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) algebra contains the standard-model and Dirac algebras as commuting subalgebras, unifying all four forces. The largest subgroup of Spin(11,1) that commutes with the Poincar\'e group is Spin(5)$\,\times\,$Spin(6), suggesting that the latter is a partial unification on the way to complete unification in Spin(11,1). The Spin(5)$\,\times\,$Spin(6) algebra contains a subalgebra with precisely the properties of the electroweak Higgs field. The Spin(5)$\,\times\,$Spin(6) symmetry contains, and is spontaneously broken by, a U(1) symmetry related to the U$_{B-L}$(1) symmetry. Grand unification is associated with a change in the dimensionality of spacetime.