> The continuity of physical processes is not something that can be proved.

I agree with you, but is there any peer-reviewed publication that can be cited? The idea makes sense to me, firstly the Reals \ Inaccessible Reals = Computable Reals, secondly you can't ever input an inaccessible real to an experiment nor retrieve one out of an experiment -- but then I'm not completely certain in making the conclusion that no experiment can be devised which shows that inaccessible reals exist in physical space.

I am concerned about this in the field of complexity analysis of quantum computers too, I think that the use of reals in physics is leading to mathematically correct but non-physical results about complexity theory of quantum computers. Having a paper to point at and say "look, stop assuming your Bloch spheres are backed by uncountable sets, it's leaking non-computable assumptions into your analysis of computation" would be helpful.