Abstract Some technical results about discontinuity and continuity of eigenprojections of reduced density operators are discussed in an elementary context. It is argued that these results suggest serious obstacles both to the goal of applying the modal interpretation to measurement theory in the context of the quantum statistical mechanics of macroscopic objects and to the goal of extending the modal interpretation to be compatible with relativistic quantum field theory. The paper is based on joint work with Guido Bacciagaluppi and Pieter Vermaas.
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