And how do you explain Aspect's experiments? Aspect's stuff shows non-classical correlation. How do you derive (or explain) the actual results without resorting to the wave function?
For example, take three polarized lenses (sunglasses are a good source); look through two of them and rotate one until no light is transmitted. Then put the other lens in between. How does the light get through now? Hard to explain without non-collapsing wave functions.
OK, Dr. Stochastic. You've hit upon an age-old scientific debate in quantum mechanics (see Roger Penrose's books, as an example for a good discussion of this). Some people take wave functions to be purely mathematical devices created by a theory which found them to be useful (like your concept of numbers). Stephen Hawking takes this approach. Others (like Penrose) believe they represent an underlying reality. But for now, it's a moot point. If they are an underlying reality, we still can't directly measure them, or changes in them (because measurement causes them to 'collapse' into reality - such as in real particles). What can be definitively said is that wave functions themselves are unmeasurable, and that one can't directly prove that they exist. You can INFER that they do, since they give rise to statistical (though NOT certain) outcomes in experiments. Whether just imaginary number functions, or some underlying reality, we can't touch, see, feel, or hear them. Yet we believe that all existence derives from them. That's how many people feel about God.
I actually tried that, and, well, it doesn't.
Hey Dr. Stochastic - forgot to answer this one. The above - Hard to explain without wave functions. But you wouldn't see any light unless the wave function collapsed. You still can only infer the existence of the (non-collapsed)wave function. You still can't touch, see, feel or hear it (or directly prove its existence). Is it real, or just a mathematical procedure? And on that note, mathematics, real and pre-existent, or just convenient human invention? (I believe the former.) And again finally, the same for many about God. Can't touch, see, or feel God, but many believe can infer existence.