Abstract
It is possible to define, for any quantum system, an algebra of ‘definite-valued events’—those events that are definitely occurrent or non-occurrent. It is shown that two different sets of constraints on the algebra of definite-valued events are each equivalent to the definition of that set as a certain ‘pseudo-Boolean’ algebra.
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References
L. Accardi (1981), ‘Topics in quantum probability’,Phys. Rep. 77:169–192.
G. Bacciagaluppi and M. Dickson (1995), ‘Modal Interpretations with Dynamics’, University of Cambridge preprint.
J. Bub (1994), ‘On the structure of quantal proposition systems’,Found. Phys. 24:1261–1279.
Bub, J. and Clifton, R. (1995) ‘A Uniqueness Theorem for Interpretations of Quantum Mechanics’, University of Maryland preprint.
J. Butterfield (1992), ‘Bell's theorem: what it takes’,Brit. J. Phil. Sci. 43:41–83.
R. Clifton (1995a), ‘Independently motivating the Kochen-Dieks modal interpretation of quantum mechanics’,Brit. J. Phil. Sci. 46:33–57.
R. Clifton (1995b), ‘Making sense of the Kochen-Dieks “nocollapse” interpretation of quantum mechanics independent of the measurement problem’,Ann. N.Y. Acad. Sci., forthcoming.
M. Dickson (1995), ‘Faux-Boolean algebras and classical models’, University of Notre Dame preprint.
D. Dieks (1989), ‘Resolution of the measurement problem through decoherence of the quantum state’,Phys. Lett. A 142:439–446.
D. Dieks (1994), ‘Modal interpretation of quantum mechanics, measurements and macroscopic behavior’,Phys. Rev. A 49:2290–2300.
A. Fine (1982a), ‘Hidden variables, joint probability, and the Bell inequalities’,Phys. Rev. Lett. 48:291–5.
A. Fine (1982b), ‘Joint distributions, quantum correlations, and commuting observables’,J. Math. Phys. 23:1306–10.
R. Healey (1989)The Philosophy of Quantum Mechanics: An Interactive Interpretation (Cambridge University Press, Cambridge).
S. Kochen (1985), ‘A new interpretation of quantum mechanics’, in P. Lahti and P. Mittelstaedt, eds.Symposium on the Foundations of Modern Physics (World Scientific, Singapore).
I. Pitowsky (1989),Quantum Probability—Quantum Logic (Springer, Berlin).
P. Vermaas (1995). ‘Transition probabilities and the modal interpretation’, University of Utrecht preprint.
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Dickson, W.M. Faux-boolean algebras, classical probability, and determinism. Found Phys Lett 8, 231–242 (1995). https://doi.org/10.1007/BF02187347
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DOI: https://doi.org/10.1007/BF02187347