Abstract
A comprehensive formal system is developed that amalgamates the operational and the realistic approaches to quantum mechanics. In this formalism, for example, a sharp distinction is made between events, operational propositions, and the properties of physical systems.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
D. Aerts, “Description of many physical entities without the paradoxes encountered in quantum mechanics,”Found. Phys. 12, 1131 (1982).
E. Beltrametti and G. Cassinelli,The Logic of Quantum Mechanics (Volume 15 ofEncyclopedia of Mathematics and its Applications), G.-C. Rota, ed. (Addison-Wesley, Reading, Mass., 1981).
G. Birkhoff,Lattice Theory (American Math. Society Colloquium Publication XXV), 3rd ed., 1967.
A. Einstein, B. Podolsky, and N. Rosen, “Can the quantum-mechanical description of physical reality be considered complete?”Phys. Review 47, 777–780 (1935).
H. Fischer and G. Rüttimann, “The geometry of the state space,” inMathematical Foundations of Quantum Theory, A. Marlow, ed. (Academic Press, New York, 1978), pp. 153–176.
D. J. Foulis and C. H. Randall, “Manuals, morphisms, and quantum mechanics,” inMathematical Foundations of Quantum Theory, A. Marlow, ed. (Academic Press, New York, 1978), pp. 105–126.
D. J. Foulis and C. H. Randall, “What are quantum logics and what ought they to be?” inCurrent Issues in Quantum Logic, E. Beltrametti and B. van Fraassen, eds. (Plenum Press, New York, 1981), pp. 35–52.
D. J. Foulis and C. H. Randall, “Empirical logic and tensor products,” inInterpretations and Foundations of Quantum Theory, H. Neumann, ed. (B. I. Wissenschaftsverlag, Bibliographisches Institut, Mannheim, 1981), pp. 9–20.
D. J. Foulis and C. H. Randall, “The empirical logic approach to the physical sciences,” inFoundations of Quantum Mechanics and Ordered Linear Spaces, A. Hartkämper and H. Neumann, eds. (Springer-Verlag, New York, 1974), pp. 230–249.
A. M. Gleason, “Measures on the closed subspaces of a Hilbert space,”J. Math. Mech. 6, 885–893 (1957).
R. J. Greechie, “On the structure of orthomodular lattices satisfying the chain condition,”J. Combinatorial Theory 4, 210–218 (1968).
P. R. Halmos,Lectures on Boolean Algebras (D. van Nostrand, Princeton, 1963).
A. A. Lodkin, “Every measure on the projectors of aW*-algebra can be extended to a state,”Functional Analysis and its Applications 8, 318–321 (1974).
B. Mielnik, “Geometry of quantum states,”Commun. Math. Phys. 9, 55–80 (1968).
B. Mielnik, “Generalized quantum mechanics,”Commun. Math. Phys. 37, 221–256 (1974).
B. Mielnik, “Quantum logic: Is it necessarily orthocomplemented?” inQuantum Mechanics, Determinism, Causality, and Particles, M. Flatoet al., eds. (Reidel, Dordrecht, 1976).
C. Piron,Foundations of Quantum Physics (W. A. Benjamin, Inc., Reading, Mass., 1976).
C. Piron, “New quantum mechanics,” inOld and New Questions in Physics, Cosmology, Philosophy, and Theoretical Biology: Essays in Honor of Wolfgang Yourgrau (Plenum Press, New York, 1983).
C. H. Randall and D. J. Foulis, “The operational approach to quantum mechanics,” inThe Logico-Algebraic Approach to Quantum Mechanics III:Physical Theory as Logical-Operational Structure, C. Hooker, ed. (Reidel, Dordrecht, 1978), pp. 167–201.
C. H. Randall and D. J. Foulis, “Operational statistics and tensor products,” inInterpretations and Foundations of Quantum Theory, H. Neumann, ed. (B. I. Wissenschaftsverlag, Bibliographisches Institut, Mannheim, 1981), pp. 21–28.
C. H. Randall and D. J. Foulis, “A mathematical setting for inductive reasoning,” inFoundations of Probability Theory, Statistical Inference, and Statistical Theories of Science III, C. Hooker, ed. (Reidel, Dordrecht, 1976), pp. 169–205.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Foulis, D., Piron, C. & Randall, C. Realism, operationalism, and quantum mechanics. Found Phys 13, 813–841 (1983). https://doi.org/10.1007/BF01906271
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01906271