Abstract
Takeuti has studied models of axiomatic set theory in which the “truth values” are elements of a complete Boolean algebra of projections on closed subspaces of a Hilbert space, and has found that the real numbers of such a model can be taken to be self-adjoint operators which can be resolved in terms of projections belonging to the Boolean algebra. It is suggested that this is the mathematical source of the replacement of real quantities by operators in quantizing a classical description, and that quantum theory involves a relativity principle with Takeuti's Boolean algebras serving as reference “frames.”
Similar content being viewed by others
References
Bohr, N. (1929).Die Naturwissenschaften 18, 73.
Jammer, Max (1974).The Philosophy of Quantum Mechanics, Wiley-Interscience, New York.
Jech, Thomas J. (1971).Lecture Notes in Set Theory, Lecture Notes in Mathematics, 217, Springer-Verlag, Berlin.
Takeuti, G. (1975). “Boolean Valued Analysis I,” preprint.
Author information
Authors and Affiliations
Additional information
This work was partially supported by the National Science Foundation under grant No. NSF MCS 76-42412.
Rights and permissions
About this article
Cite this article
Davis, M. A relativity principle in quantum mechanics. Int J Theor Phys 16, 867–874 (1977). https://doi.org/10.1007/BF01807619
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01807619