What is the wavefunction?
The wavefunction is a way of writing down what an observer can ask and the odds of each answer. What an observer actually holds is a list of yes-or-no questions plus a state, a rule that gives every question a probability. Put the two together and they generate a space of arrows, and the wavefunction is an arrow in that space. Its entries are amplitudes, numbers carrying a turning phase, so they can cancel where probabilities never could, and probabilities are their squares. Different observers with different lists of questions build different spaces, and they agree wherever their lists overlap. That overlap is the only sense in which the wavefunction is public. An electron's wave is recovered from agreed records after the fact. It was never sitting in the tube waiting to be sampled.
Also in Chapter 28: What Is a Particle, What Is a Wave, and Why Does It Look Like Both?.
This answer comes from OPH, Observer Patch Holography. OPH is a rigorous, consistent and complete description of the unified, self-creating computational Universe we inhabit. Its consistency is machine-checked: the fixed point at its core is constructed explicitly, and a theory with a model contains no contradiction.
To understand OPH and check every step yourself, start with the free book Reverse Engineering Reality. It builds the theory from the ground up, and the OPH Notebook answers your questions while you read.
read the free bookask the notebookor ask sage:read chapter 19: Why Can't You Ask Everything At Once?watch a universe make its own particles