The limitations of existing methods of modal interpretation are highlighted, and an insight into the mode selection for response analysis is provided.
In this case, in which the definite-valued properties selected by a modal interpretation are different from those expected, the question arises how different they are.
In spite of the fact that this modal interpretation is characterized by the central role played by biorthogonal decomposition, two different versions can be distinguished.
Yet, as the no-go theorems by Dickson and Clifton (1998), Arntzenius (1998) and Myrvold (2002) demonstrate, the earlier versions of the modal interpretation are not genuinely compatible with relativity theory.
The challenge for this atomic modal interpretation is to justify the assumption that there is a preferred partition of the universe, and to provide some idea about how such factorization should look like.
Thus, the modal interpretation is not committed to actual mathematical structures; there is no commitment to their existence as objects or to any objects that happen to 'constitute' these structures.
Indeed, it appears that in more general models of decoherence the components singled out by this version of the modal interpretation are given by delocalised states, and are unrelated to the localised components naturally privileged by decoherence (Donald 1998; Bacciagaluppi 2000).
