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We evaluate the first claim in the context of a simple spin bath model. We find that even for large environments, corresponding to an approximately continuous energy spectrum, diagonalization of the expectation value of random observables does in general not occur. We explain this result and conjecture that SID is likely to fail also in other systems composed of discrete subsystems. Regarding the second claim, we emphasize that SID does not describe a physically meaningful decoherence process for individual measurements, but only involves destructive interference that occurs collectively within an ensemble of presupposed \"values\" of measurements. This leads us to question the relevance of SID for treating observed decoherence effects."},{"label":"DOI","value":"10.1103/PhysRevA.72.012109"},{"label":"Volume","value":"72"},{"label":"Publication Date","value":"D:00 M:00 Y:2005"},{"label":"Publication Information","value":"Copyright 2005 American Physical Society. 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