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.
Similar content being viewed by others
References
Aleksandrov, A. D. (1955). The space-time of general relativity.Helv. Phys. Acta,4(Suppl.), 4.
Chevalley, C. (1955). The construction and study of certain important algebras,Math. Soc. Japan.
Finkelstein, D. (1972). Space-time code. II,Phys. Rev. D,5, 2922.
Finkelstein, D. (1982). Quantum sets and Clifford algebras,Int. J. Theor. Phys.,21, 489.
Pimenov, R. I. (1968).Spaces of Kinematic Type, Steklov Mathematical Institute, Leningrad (in Russian; translated into English and published by Consultant's Bureau, New York).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Finkelstein, D., Rodriguez, E. The quantum pentacle. Int J Theor Phys 23, 887–894 (1984). https://doi.org/10.1007/BF02214072
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02214072