Quantum Logic and Ensembles

  • Peter Gibbins
Part of the Synthese Library book series (SYLI, volume 157)


Probability, as it appears in quantum mechanics, is a measure on the non- boolean lattice of propositions known as quantum logic. It is therefore no surprise that quantum probability is non-classical and that attempting to impose on quantum probability a classical ensemble interpretation leads to paradox. One such paradox is provided by the ignorance interpretation of mixtures, another by the Einstein-Podolsky-Rosen (EPR) thought-experiment. I shall argue, in reply to Dr. Redhead, that a quantum logical ensemble (QLE) interpretation of quantum mechanics resolves these paradoxes in a natural way and that in the case of the EPR paradox one need not invoke superluminal causal connections to account for the non-locality. This paper therefore has somewhat narrower scope than Dr. Redhead’s for I shall have no need to examine tachyonic mechanisms to explain the EPR correlations.


Density Operator Quantum Logic Individual System Quantum Probability Spin Measurement 
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  1. Ballentine, L. E.: 1970, ‘The Statistical Interpretation of Quantum Mechanics’, Rev. Mod. Phys. 42, 358.CrossRefGoogle Scholar
  2. Bohm, D.: 1951, Quantum Theory, Prentice-Hall.Google Scholar
  3. Einstein, A., Podolsky, B., and Rosen N.: 1935, ‘Can Quantum Mechanical Description of Reality be considered Complete?’, Phys. Rev. 47, 777.CrossRefGoogle Scholar
  4. van Fraassen, B.: 1972, ‘A Formal Approach to the Philosophy of Science’, in Paradigms and Paradoxes, R. Colodny (ed.), Pittsburgh, pp. 303–366.Google Scholar
  5. Grossman, N.: 1974, ‘The Ignorance Interpretation Defended’, Phil. Sci. 41, 333.CrossRefGoogle Scholar
  6. Hooker, C.: 1972, ‘The Nature of Quantum Mechanical Reality’, in Paradims and Paradoxes, op. cit. pp. 67–302.Google Scholar
  7. Jauch, J. M.: 1968, Foundations of Quantum Mechanics, Addison-Wesley.Google Scholar
  8. Park, J. L.: 1968, ‘Nature of Quantum States’, Am. Joum. Phys. 36, 211.CrossRefGoogle Scholar
  9. Popper, K.: 1971, ‘Particle Annihilation and the Argument of Einstein, Podolsky and Rosen’, in Perspectives in Quantum Theory, Yourgrau W. and van der Merwe A. (eds.), Dover Books, pp. 182–198.Google Scholar
  10. Redhead, M. L. G.: 1981, ‘Experimental Tests of the Sum Rule’, Phil. Sci. 48, 50.CrossRefGoogle Scholar

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© D. Reidel Publishing Company 1983

Authors and Affiliations

  • Peter Gibbins

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