A Dilemma for the Traditional Interpretation of Quantum Mixtures

Abstract

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.