[calf]

I've read this thread exchange with interest, but what about the results that quantum computers are simulatable by classical computers? See David Deutsch 1985. This would reduce the issue of infinite Hilbert spaces to simulation using quantum computers, and in turn, Deutsch's result which says classical Turing machines can actually simulate quantum computers.

[mjburgess]

You can always make local arguments that, say, some g can be substituted with some c.

The issue is broader than that. It concerns the premises of vast areas of physics -- you have to show they are more likely false than true.

This isnt an argument saying no c can be found for any given g, it's saying, "g-c gaps have empirical consequences we havent observed" and if we did, physics would be foundationally wrong

[calf]

When they assert theorems like "classical TMs can simulate quantum TMs" they mean the simulation is gapless. Otherwise they use the term approximation.