Elementary Operations

Abstract

A Clifford algebra over the binary field 2 = {0,1} is a second-order classical logic that is substantially richer than Boolean algebra. We use it as a bridge to a Clifford algebraic quantum logic that is richer than the usual Hilbert space quantum logic and admits iteration. This leads to a higher-order Clifford-algebraic logic. We formulate a toy Dirac equation with this logic. It isexactly Lorentz-invariant, yet it approximates the usual Dirac equation as closely as desired and all its variables have finite spectra. It is worth considering as a Lorentz-invariant improvement on lattice space-times.