In this chapter we shall discuss a variety of topics that are not covered by Sewell's scheme. Our main conclusion will be that Sewell's scheme can be extended to cover these topics, and the extension provides adequate answers to the problems of measurement theory in quantum mechanics. We shall then attempt to meet the last three of Wigner's objections listed on page 158, and the problem arising from the failure of localizability in relativistic physics that was stressed by him. The material will be arranged as follows.

In Section 11.1 we shall deal with an example of Bell that challenged the notion of quantum mechanics as it has been used so far in this book. In Section 11.2 we shall discuss a few extensions of Sewell's scheme, leaving aside the crucial extension to continuous spectra. That discussion, provided in Section 11.6, will be preceded by short accounts of the results of Araki and Yanase in Section 11.3, the impossibility theorems of Shimony and Busch in Section 11.4, and the Heisenberg cut in Section 11.5. The results of Araki and Yanase were obtained within von Neumann's measurement theory proper,1 whereas Shimony and others based their attempts on a class of modifications of it. Section 11.7 will be devoted to establishing the adequacy of Sewell's scheme, and Section 11.8 to meeting the objections of Wigner and providing our answer to the question that has induced the writing of Part II of this book.