It implies an a priori background structure. Hilbert spaces are usually preferred, as the complex state of a wavefunction kind of implies that representation.
so i think that's actually part of what I found notable about one of the posed hypotheses nearer the end of the video - the complex nature of the wavefunction essentially gets transformed into a 'more intuitive' lattice node space-like rotation within the Kleinert elastic crystal model. which, as someone who spent a short time 'getting used to' qm, seems very tempting.
plus, dont Hilbert spaces assume they are infinitessimally detailed (ie: complete)? which seems like it could lead to potential collisions with set-theoretic geometry, eg possibly some potential for a physical manifestation of the banach-tarski paradox, which would clearly violate conservation laws
plus, dont Hilbert spaces assume they are infinitessimally detailed (ie: complete)? which seems like it could lead to potential collisions with set-theoretic geometry, eg possibly some potential for a physical manifestation of the banach-tarski paradox, which would clearly violate conservation laws