Evening conversations (contd.)

52:30 The assumption, the default assumption, I would love to understand this whole subject of those people, well actually Mackey equally, Mackey in particular perhaps, for the impact of functional analysis on foundations of physics because it seemed to me ever since I'm aware of this whole theory of some sort of unbounded operators in this space that there was something... What is wrong in the default assumption that Hilbert space is the correct state of space for the rotation of the systems of quantum mechanics? Even apart from the fishy physical assumptions that this linear mechanics holds right the way down, there's also an even equally fishy question about what should be the correct default category for this.

55:00 And that Fretendeet's work on Hilbert spaces should have alerted us a long time since to the fact that... There's something wrong about Hilbert's category. It would be bad as a setting for dynamics. Curiously, the great names, Dirac is one example, but von Neumann himself, actually, was obsessed with the Hilbert space formalism and thought that it would have to be abandoned. Dirac, much earlier and more explicit, but von Neumann too. It was about 1936, he already said, and in print, that he thought that the Hilbert space formalism was simply nonsense.