PSA 1972 pp 251-258 | Cite as

A Dilemma for the Traditional Interpretation of Quantum Mixtures

  • Nancy Cartwright
Part of the Boston Studies in the Philosophy of Science book series (BSPS, volume 20)


This paper argues that the ignorance interpretation of mixtures is physically unrealistic. The ignorance interpretation is the orthodox interpretation for mixtures, and should not be confused with the ignorance interpretation for superpositions, which has been largely abandoned. Mixtures, unlike superpositions, do not interfere. They are represented by mixed (or non-idempotent, i.e. W 2 ≠W) operators; superpositions, by pure (or idempotent) operators or by vectors. In the minimal interpretation both pure and mixed operators may be taken to describe collections. Any pure state, ψ, may be expressed as a sum of other pure states, Ø 1, Ø 2,..., Ø n. Yet we cannot postulate that the members of the collection described by ψ are each in one of the pure states Ø 1, Ø 2,...;, Ø n. This is because of the interference between the pure states Ø 1..., Ø n. On the other hand, if we have a mixture of Ø 1..., Ø n, we can consistently postulate that the members of the collections are each in one of the pure states Ø 1..., Ø n.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Neumanm, John von, The Mathematical Foundations of Quantum Mechanics, (trans, by R. Beyer), Princeton University Press, Princeton, 1955.Google Scholar
  2. 3.
    Feyerabend, P. K., ‘On the Quantum Theory of Measurement’, Observation and Interpretation, (ed. by S. Körner), Academic Press, New York, 1957, pp. 121–130.Google Scholar
  3. 4.
    Fano, U., ‘Description of States in Quantum Mechanics by Density Matrix and Operator Techniques’, Reviews of Modern Physics 29 (1957) 74ff.CrossRefGoogle Scholar

Copyright information

© D. Reidel Publishing Company, Dordrecht-Holland 1974

Authors and Affiliations

  • Nancy Cartwright
    • 1
  1. 1.University of MarylandUSA

Personalised recommendations