Abstract
Working in a quantum logic framework and using the idea of Galois connections, we give a natural sufficient condition for superposition and inaccessibility to give the same closure map on sets of states.
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References
Abbott, J. (1969).Sets, Lattices and Boolean Algebras, Wiley, New York.
Bell, J. (1966). On the problem of hidden variables in quantum mechanics,Review of Modern Physics,38, 447–452.
Bohm, D., and Bub, J. (1966). A refutation of the proof by Jauch and Piron that hidden variables can be excluded in quantum mechanics.Review of Modern Physics,38, 470–475.
Beltrametti, E., and Cassinelli, G. (1976). Logical structures arising in quantum mechanics.Nuovo Cimento,6, 321–390.
Beltrametti, E., and Cassinelli, G. (1981).The Logic of Quantum Mechanics, Addison-Wesley, Reading, Massachussets.
Blyth, T., and Janowitz, M. (1971).Residuation Theory, Pergamon Press, Oxford.
Foulis, D. (1960). Baer*-semigroups,Proceedings of the American Mathematical Society,11, 648–654 [reprinted in Hooker (1975)].
Gudder, S. (1970). A superposition principle in physics,Journal of Mathematical Physics,11, 1037–1040.
Guz, W. (1978). On the lattice structure of quantum logics,Annales de l'Institut Henri Poincaré,28, 1–7.
Hooker, C., ed. (1975).The Logico-Algebraic Approach to Quantum Mechanics, Volume 1, Reidel, Dordrecht, Holland.
Jammer, M. (1974).The Philosophy of Quantum Mechanics, Wiley, New York.
Jauch, J., and Piron, C. (1963).Helvetica Physica Acta,36, 827.
Ore, O. (1944). Galois connections,Transactions of the American Mathematical Society,55, 493–513.
Pool, J. (1968). Baer*-semigroups and the logic of quantum mechanics,Communications on Mathematical Physics,9, 118–141 [reprinted in Hooker (1975)].
Pták, P., and Pulmannová, S. (1991).Orthomodular Structures as Quantum Logics, Kluwer Academic, Dordrecht, Holland.
Varadarajnn, V. (1968).The Geometry of Quantum Theory, Volume 1, Princeton University Press, Princeton, New Jersey.
Zierler, N. (1961). Axioms for non-relativistic quantum mechanics,Pacific Journal of Mathematics,11, 1151–1169 [reprinted in Hooker (1975)].
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Butterfield, J., Melia, J. A Galois connection approach to superposition and inaccessibility. Int J Theor Phys 32, 2305–2321 (1993). https://doi.org/10.1007/BF00673001
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DOI: https://doi.org/10.1007/BF00673001