Psy-Kosh, when QM is formulated rigorously (something that is rarely done, and only by mathematical physicists) the amplitudes must be able to take on any number in the complex plane, not just the rationals.

Sebastian Hagen, I believe Eliezer is explaining to us the best model physicists have for the way the world works on the (sorta) lowest level we understand, not his personal beliefs on the nature of reality. This model must include the irrationals, to be self-consistent. This does not prevent the universe from being discretized (no uncountable sets) on a more fundamental level from QM.

I guess, Eliezer, that I would be concerned about convincing everyone that the universe runs along like a computer, computing amplitudes locally (which seems to be the gist of your discussion). To do so would certainly make people *feel* like QM isn't confusing; it would just be wave mechanics. But this would give people a false confidence, I think, and is not how the universe appears to operate.

But this is the first post, so I'll try to confine my criticism until you've wrapped up your discussion.

Eliezer, in case you plan to discuss Bell's-inequality-type experiments in future posts, I suggest that you use the GHZ state (not the EPR pair) to show how local realism is ruled out in QM. The GHZ state is a much cleaner result, and is not obscurred by the statistics inherent in Bell's inequality.