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.
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.