x}$, the separation four-vector between them must have norm $\|x\|^2 < 0$ in the ${\bf R}^{3,1}$, space (or $\|x\|^2 > 0$ in the ${\bf R}^{1,3}$ space). Equivalently, we way that the vector connecting an event with its cause is [*timelike*]{}, or lies inside the [*light cone*]{} (the hypersurface for which $\|x\|^2=0$).

The Clifford algebra generated by the four basis vectors in the “east coast” $(+++-)$ metric is known as the [*Majorana algebra*]{}, with matrix representation ${\bf R}(4) = \endo{3,1}$. This algebra is different to that generated by the other metric choice (used for example by Hestenes[@Hestenes82]), which has inequivalent matrix representation ${\bf H}(2) =\endo{1,3}$, i.e.$2 \times 2$ quaternionic matrices[@Porteous]. Regardless, either algebra has 16 basis elements, but contains the global commuting $i$, which is usually required by physicists for standard relativistic quantum mechanics[@Drell64]. Those theories use the “classic” [*Dirac algebra*]{}, which has anticommuting generators $\{\gamma^{\mu}\}$, corresponding to complex matrix representation ${\bf C}(4)= {\bf C}\otimes {\bf H}(2) =  {\bf C}\otimes {\bf R}(4)$.

The “projection” or [*spacetime split*]{} from ${\tt 4D \rightarrow 3\oplus 1}$ can be encoded algebraically in ${\bf R}(4)$, $$-{\bf x} \ \basis{4} = \vector{X} + t, \eqno(2.4)$$ where the Pauli algebra generators $\sigma_j$ of eq. (2.1) are related to 