When I was a naive student first getting interested in physics, I was awed by its predictive power and took the theories themselves to be reality. On the blog Cosmic Variance Sean Carroll promotes this viewpoint when he writes:
"Right and wrong aren’t parts of the fundamental description of reality. That description has to do with wave functions and Hamiltonian dynamics, not with ethical principles. That is what the world is made of, at a deep level."
This is exactly how I used to think about things. Lately though, I have become more of a positivist. This is the viewpoint that scientific theories are just models. A good model makes predictions that agree with experiment. The fact that the models often change with time as better data or ideas come to the fore shows that its naive to take the models as absolute descriptions of reality. For a simple example you might consider the Bohr atom. If you recall, Bohr thought of the atom as a little solar system, with the nucleus playing the role of the sun and electrons occupying fixed orbits at different distances from the nucleus. As they jumped from one orbit to another, they emitted or absorbed photons of light.
We now know an atom isn't quite like that, and that instead the wave function of the electron allows us to make probabilistic predictions as to where the electron will be found. Each orbit is described by a different wave function, giving the "electron cloud" picture of the atom. The Bohr model of the atom, even though it agrees with a lot of experimental data, isn't real.
The positivist would say that the electron cloud is no more reality than Bohr's atom was. It simply makes better predictions. At our current level of technology and predictive capability, it seems to work perfectly. But that doesn't mean that in the future a better model of the atom won't come about. And-despite its drawbacks-the Bohr model of the atom actually works quite well in many circumstances. In nuclear engineering its often if not always adequate enough to think of the atom in terms of Bohr's picture. On the other hand, if you're doing quantum chemistry then you need to think in terms of the electron cloud model.
This goes to show that taking "wave functions" and "Hilbert space" to be reality itself is a naive viewpoint. Wave functions and Hilbert space are just tools that allow scientists to make predictions. They are good tools to be sure, but confusing a good tool that exists on paper and only in the minds of arrogant physics professors to be fundamentally real is an extremely naive approach to life.
The positivist viewpoint makes a lot more sense. Stephen Hawking summed it up well in his best seller A Brief History of Time when he wrote:
"Any sound scientific theory, whether of time or of any other concept, should in my opinion be based on the most workable philosophy of science: the positivist approach put forward by Friedrich Hayek and Karl Popper and others. According to this way of thinking, a scientific theory is a mathematical model that describes and codifies the observations we make. A good theory will describe a large range of phenomena on the basis of a few simple postulates and will make definite predictions that can be tested… If one takes the positivist position, as I do, one cannot say what time actually is. All one can do is describe what has been found to be a very good mathematical model for time and say what predictions it makes."
At the time I read this back in 1990, I was disappointed Hawking felt this way. Now with some maturity under my belt I realize that this is a far better description of what science does than taking some equations on a blackboard-which are good, useful tool to be sure-to really be reality itself.