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MrMind comments on Open Thread, November 15-22, 2013 - Less Wrong Discussion
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There has been some attempts at categorizing infinite-dimensional quantum physics.
While finite-dimensional quantum physics is pretty much categorized (symmetric monoidal dagger categories, see the works of Coecke and Abramsky), the infinite version is still in its infancy.
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.
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.
There are already examples of quantum theories with multiple interpretations, most famously AdS/CFT. Do these affect your view of realism?