The quantum pentacle

Abstract

Quantum set theory permits the formulation of a quantum simplicial topology suitable for a quantum theory of time space and gravity without prior time space structure. The quantum simplex differs strikingly from the classical: It is isotropic (“points in all directions”) and all quantum simplexes of the same signature are congruent. Quantum simplexes and complexes are described byS numbers, elements of the Clifford algebra of quantum sets. The isotropy groups of noncontiguous simplexes commute, like local invariance groups in a gaugeinvariant theory.