On the physical impossibility of ideal quantum measurements

Albert and Loewer have argued in this journal [4] that modal interpretations of quantum mechanics are ruled out if the abstract structure of Hilbert space is taken realistically. Their argument contains a dubious inference from a measure-zero set of non-ideal interactions. I look at possible ways to make this inference valid and I conclude that the evidence against the modal interpretation cannot be found in the Hilbert space alone. Instead an analysis of specific cases is required.