Understanding wave functions I'm currently writing an essay on the measurement problem, and I'm not quite certain that I've fully understood the purpose of the wave function, in that does the following sentence make sense with respect to the wave function:

Although the wave function itself is never physically observed, we are given resultant macroscopic events which we can interpret, allowing us to formulate a conclusion.

What I mean to say is that although we don't actually see the wave function, we can see the kind of after-math of what happens in the form of a physical macroscopic event..is that right?
 A: In short, yes, you can see the "effects" of a wavefunction after some math, but never "see" the "actual wavefunction." Wavefunctions are not physical things. Let me explain:
If you take the complex conjugate of a wavefunction, you get a function which can tell you the odds of finding a particular particle at a place at a certain time. If you do other math to it, you can get energies of the particle and other properties (like spin). If you take that wavefunction into a lab, you can make predictions about what your experiment will do, and smile at an unlikely but still predicted result. You should note, however, that a wavefunction alone does not mean probability, it does not mean energy, nor does it mean position. It's a mathematical concept, a collection of marks on a physicist's notebook, as real as a country's Gross Domestic Product or the number of cats GIFs downloaded per click from a particular computer. Like all those things, they are not physical things.
Anyways, the issue here is that people often feel that these physics concepts must be tangible "things." Wavefunctions, energy, and entropy are not things you directly experience. They are concepts; mathematical constructions we use to account for what can happen in the universe. You can see the effects of entropy, you can see the effects of high or low energies, and you can see the effects of wavefunctions. You cannot, however, "see" these concepts because they don't exist like a force or property of matter. These "higher" concepts are just how we keep track of things going on in the universe, and wavefunctions are very complicated accountant's notes. You can try to think of wavefunctions as actual things, bouncing around the universe, but then you'll be flummoxed once and forever, because they are not physical things.
If we come up with a better way of tracking the universe, we may one day discard wavefunctions. It could be totally abandoned, becoming entombed in an infrequently visited wikipedia page, a stepping stone to some greater understanding. If that happens, the actual, physical universe would not change at all. We would just understand it better under some other accounting system.
