CONTINUITY AND DISCONTINUITY OF DEFINITE PROPERTIES IN THE MODAL INTERPRETATION

Technical results about the time dependence of eigenvectors of reduced density operators are considered, and the relevance of these results is discussed for modal interpretations of quantum mechanics which take the corresponding eigenprojections to represent definite properties. Continuous eigenvectors can be found if degeneracies are avoided. We s how that, in finite dimensions, the space of degenerate operators has co-dimension 3 in the space of all reduced operators, suggesting that continuous eigenvectors almost surely exist. in any dimension, even wh en degeneracies are hit, we find conditions under which a theorem due to Rellich can provide continuous eigenvectors. We use this result to formulate an extended version of the modal interpretation. We also dis cuss eigenvector instability which we argue poses a serious problem fo r the modal interpretation, even in our extended version. Many example s are given to illustrate the mathematics.