Abstract
Birkhoff and von Neumann's famous paper, “The Logic of Quantum Mechanics”, culminates in a proposal which clashes with each of a number of assumptions made by the authors. A thought experiment, intended to show the need for the proposal, is rejected.
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References
Birkhoff, G., and von Neumann, J., Ann. of Math., 37, 823 (1936).
von Neumann, J., Lectures on Continuous Geometries, theorems 5.3 and 5.4, vol. 1 (Princeton Univ. Press, 1936–7). See also Birkhoff, G., Lattice Theory, second ed., 171 (American Mathematical Society, 1948), and Dilworth, R. P., Bull. Amer. Math. Soc., 46, 74 (1940).
Birkhoff, G., and Ward, M., Ann. of Math., 40, 609 (1939). See also Birkhoff, G., Lattice Theory, second ed., 170 (American Mathematical Society, 1948).
Birkhoff, G., Lattice Theory, first ed., 94 (American Mathematical Society, 1940); second ed., 171 (American Mathematical Society, 1948).
Tarski, A., Logic, Semantics, Metamathematics, Theorem 11, 45 (Oxford Univ. Press, 1956).
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POPPER, K. Birkhoff and von Neumann's Interpretation of Quantum Mechanics. Nature 219, 682–685 (1968). https://doi.org/10.1038/219682a0
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DOI: https://doi.org/10.1038/219682a0
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