>The fact that the model is a continuous real function is an artifact of the model, a weakness not a strength. The wave function is the square root of a probab

>The fact that the model is a continuous real function is an artifact of the model, a weakness not a strength. The wave function is the square root of a probability distribution. The wavefunction is a continuous real function of position because position is modeled as a continuous real variable. The idea of the wavefunction as a function of position is generally supported by the fact that it can be used to predict the measurement results of diffraction experiments like the double-slit experiment, but also practically the whole field of X-ray diffraction. There is not just one experimental result that is explained by wavefunctions. There are widely used measurement techniques whose outcomes are calculated according to the quantum properties of matter — like X-ray diffraction and Raman scattering — which are widely considered to be extremely reliable. There is a good reason to explain the model of reality expressed by the equations as clearly as possible, because we want people to be able to use the equations. Plenty of people (though certainly not all) expect quantum mechanics to be eventually modified to have a consistent theory of gravity. But physicists have experience with this. Special relativity and classical quantum mechanics were both more complex than Newtonian (classical) mechanics, and quantum field theory is more complicated than either. General relativity is substantially more involved than special relativity. It is likely that further extensions will continue to get worse. The model of reality taught by Newtonian (classical) mechanics is also still widely discussed and used in introductory physics courses and many areas of physics (such as fluid dynamics) and engineering. This model also discusses position on the real line. Even though classical mechanics had to be modified, the use of Cartesian coordinates and real numbers turned out to be durable. Usually the finitists will formally "rescue" countability by suggesting that the world could exist on the computable numbers, which are countable and invariant under computable rotations. But the computable numbers are a very unsatisfying model of reality, and have a lot of the same "weirdness" as the real numbers. Therefore they suggest that some other model must exist without giving a lot of specifics. Why this should be somehow helpful and not injurious to the pedagogy of physics is not clear.