New essay. New essay that shows how the linearity of the vector space representation is a mathematical convenience, not a physical requirement. It’s based on this brief, which has all technical details. I am experimenting in leaving the essay less technical, just describing the results and their significant, while having all technical details (and LaTeX!) in the technical briefs in a more terse form.
New briefs. Added another three briefs. They are all on identifying the correct state space for quantum mechanics, since Hilbert spaces do not quite work. First one shows how the expectation of all monomials of position and momentum do no identify a Schwartz function (i.e. the momentum problem does not, in general, admit a unique solution in Schwartz space). Second one shows that the sup-norms, L^1, L^2 seminorms generate the same topology on Schwartz spaces. The third shows that the entropy is not continuous in the standard topology one uses in both classical and quantum probability. The first and the third is something I was actually wrong on (I like proving myself wrong!)… but the third one was more unexpected, and I have to fix a couple of things in the ensemble space chapter.
Live on symplectic group and uncertainty. We had a live yesterday where Najim discussed his progress on mapping the symplectic group in a way that will hopefully allow us to describe how the uncertainty evolves in Hamiltonian evolution.
That’s it for this week!
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