Quantum elements of time and space

Space-times of any number of spaces and times can be generated as tensor products of a time-like unit vector \textbf{T} and a space-like unit vector \textbf{S}. \textbf{T} is a $2\times 2$ real anti-symmetric, hence trace-free, matrix squaring to $\mathbf{-I}$; \textbf{S} is a $2\times 2$ real symmetric trace-free matrix squaring to $\mathbf{+I}$. \textbf{T} is unique up to sign, corresponding to particles and antiparticles. \textbf{S} is a qubit whose eigenvalues are the bits $+1$ and $-1$. Thus the quantization of space is rotationally invariant in $2d$ and Lorentz invariant in $4d$. Use \textbf{S} instead of complex numbers \textbf{C} to geometrize quantum mechanics. The simplest space-time is the Minkowskian plane with vectors \textbf{T} and \textbf{S}, which generate a geometric algebra \{\textbf{I},\textbf{T},\textbf{S},\textbf{ST}\}, where the bivector \textbf{ST} is space-like. It can be used as vector \textbf{X} for the Euclidean plane, along with \textbf{Y}=\textbf{S}. They generate a geometric algebra \{\textbf{I},\textbf{X},\textbf{Y},\textbf{YX}\}. The bivector \textbf{YX} is \textbf{T}. The Minkowskian plane and the Euclidean plane have different geometries but the same geometric algebra, which is thus the foundation of both general relativity and quantum mechanics.