Hostname: page-component-cd9895bd7-lnqnp Total loading time: 0 Render date: 2024-12-26T00:38:34.690Z Has data issue: false hasContentIssue false
  • English
  • Français

The Tensor Product of Operational Logics

Published online by Cambridge University Press:  20 November 2018

Robin H. Lock
Robin H. Lock*
Affiliation:
St. Lawrence University, Canton, New York
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The concept of an operational logic has been developed by Randall and Foulis ([l]-[4], [10], [11]) as a part of a larger effort to obtain a formalism suitable for expressing, comparing, and evaluating various approaches to empirical science, statistics, and in particular, quantum mechanics. The structure of these logics is similar to that of an orthomodular partially ordered set which is often used as a model for quantum logics. However, the operational logic is a more general structure which, among other features, allows for the creation of a tensor product of logics to represent the coupling of physical systems. Randall and Foulis have shown that, given certain reasonable physical constraints, such a product is not possible within the category of orthomodular posets [12].

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 38 , Issue 5 , 01 October 1986 , pp. 1065 - 1080
Copyright
Copyright © Canadian Mathematical Society 1986

References

1. Foulis, D. J. and Randall, C. H., The empirical logic approach to the physical sciences, in Foundations of quantum mechanics and ordered linear spaces, Lecture Notes in Physics 29 (Springer-Verlag, New York, 1974).Google Scholar
2. Foulis, D. J. and Randall, C. H., Manuals, morphisms, and quantum mechanics, in Mathematical foundations of quantum theory (Academic Press, New York, 1978).Google Scholar
3. Foulis, D. J. and Randall, C. H., Empirical logic and tensor products, Proceedings of the Colloquium on the Interpretations and Foundations of Quantum Theories, Fachbereich Physik der Philipps Universitat, Marburg, Germany (1979).Google Scholar
4. Foulis, D. J. and Randall, C. H., What are quantum logics and what ought they to he?, Proceedings of the Workshop on Quantum Logic, Ettore Majorana Centre for Scientific Culture, Erice, Sicily (1979).Google Scholar
5. Halmos, P. R., Lectures on Boolean algebras, 25 (Van Nostrand 1958).Google Scholar
6. Hardegree, G. and Frazer, P. J., Charting the Labyrinth of quantum logics; a progress report, Proceedings of the Workshop on Quantum Logic, Ettore Majorana Centre for Scientific Culture, Erice, Sicily (1979).Google Scholar
7. Lock, P. F., Categories of manuals, Ph.D. dissertation, University of Massachusetts (1981).Google Scholar
8. Lock, P. F. and Lock, R. H., Tensor products of generalized sample spaces, International Journal of Theoretical Physics 23 (1984).Google Scholar
9. Lock, R. H., Constructing the tensor product of generalized sample spaces, Ph.D. dissertation, University of Massachusetts (1981).Google Scholar
10. Randall, C. H. and Foulis, D. J., The operational approach to quantum mechanics, in Physical theory as logico-operational structure (D. Reidel Publishing Co., Dordrecht, Holland, 1978).CrossRefGoogle Scholar
11. Randall, C. H. and Foulis, D. J., Operational statistics and tensor products, Proceedings of the Colloquium on the Interpretations and Foundations of Quantum Theories, Fachbereich Physik der Philipps Universitat, Marburg, Germany (1979).Google Scholar
12. Randall, C. H. and Foulis, D. J., Tensor products of quantum logics do not exist, Notices of the Amer. Math. Society 26 (1979).Google Scholar