It is quantum which isn’t exactly discrete. You receive one photon or two, not 1.5, sure, but the energy of that photon, its frequency is a real. At least I am

It is quantum which isn’t exactly discrete. You receive one photon or two, not 1.5, sure, but the energy of that photon, its frequency is a real. At least I am not aware of a quantum mechanics over Q. I think the math would be hard because you loose all the convergence properties. Maybe there is some Hilbert space over computable reals, Google is not finding it but I no longer find that to be indicative of anything.