Abstract
We define a physical magnitude as an equivalence class of measurement procedures and formulate sufficient restrictions on the equivalence relation to guarantee meaningful algebraic operations between magnitudes. These restrictions are not sufficient to let the Kochen and Specker argument go through. They are, however, stronger than mere statistical equivalence of measurement procedures and thus are relevant to the problem of the completeness of quantum mechanics. In fact, they give rise to a strong argument for the incompleteness of quantum mechanics.
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References
S. Kochen and P. Specker, inThe Logico-Algebraic Approach to Quantum Mechanics, C. A. Hooker, ed. (Reidel, Boston, 1975), p. 293.
A. Fine and P. Teller,Found. Phys. 8, 629 (1978).
A. Fine,Synthese 29, 257 (1974).
R. M. Cooke and J. Hilgevoord, Splitting Quantum Magnitudes: An Approach to Hidden Variables; with Applications to the Theorems of Kochen and Specker (in preparation).
R. Latzer,Synthese 29, 331 (1974).
B. C. Van Fraassen, inContemporary Research in the Foundations and Philosophy of Quantum Theory, C. A. Hooker, ed. (Reidel, Boston, 1973).
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Cooke, R.M., Hilgevoord, J. The algebra of physical magnitudes. Found Phys 10, 363–373 (1980). https://doi.org/10.1007/BF00708739
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DOI: https://doi.org/10.1007/BF00708739