If a fully quantum category will be found, and showed to have more than one model, then I think that the idea of reality as an infinite-dimensional configuration space inhabited by an atemporal wave-function should be abandoned.
Because then any model of the full quantum category would describe the same reality: instead of the infinite-dimensional Hilbert space you could just choose say a much looser ontology with sets and relations between them (as in Spekken’s toy model of quantum physics). This arbitrariness would undermine the raison d’etre of the present model.
Why?
Because then any model of the full quantum category would describe the same reality: instead of the infinite-dimensional Hilbert space you could just choose say a much looser ontology with sets and relations between them (as in Spekken’s toy model of quantum physics).
This arbitrariness would undermine the raison d’etre of the present model.