I'm taking on an interesting task: explaining to an extremely advanced 11 year old that much of what he hears and reads from the "popular physics" videos and TV programs isn't accurate, and some of it is just wrong. I know I have a problem here however - once he moves on to high school physics he's going to come across many of these same incorrect explanations from his teachers. I need to decide if I go so far as to explain that there is ZERO evidence showing or theorizing that an electron (for instance) is ever a wave.
He's bright as heck, and I can certainly explain a probability function, and can explain that it's a solution to a wave equation. And I can explain that this probability function is NOT the electron itself. And that this probability function can be plotted in a way that it can look like a wave or a superposition of waves. But do I stop there or continue and say simply "this does not in any way imply that the electron itself is a wave!"
If I was that kid I would have LOVED it if someone explained this to me at an early age. But I know I would have upset some teachers. Maybe only once or twice though. I'd like to know what everyone else thinks.
From the comments I realize there's a need to modify my question with the following statement:
The probability function (or superposition thereof) has meaning because it is the solution to a very special wave equation that has proven to glean incredible meaning. The electron is and never has been a solution to such a special wave equation. We can learn things about electron behavior from the solutions to this wave equation, but it makes no sense to say that the electron is a solution to this same wave equation.
Furthermore, to posit that ANY localized entity is a wave is disingenuous and misleading: Propose any thing which can be plotted and/or described as a function, and I will show you a superposition of orthogonal solutions of SOME equation that will describe it to whatever precision that seems reasonable (let's say "measurable" for these purposes). If I choose that equation to be a wave equation then I allow myself the right to call the thing a wave and give it a wavelength which quantifies some average spatial distribution. Is that meaningful? Does that help us to understand an electron? I say no.
Yes - I do strongly believe that there is NO reason to call the electron a wave ever, because there is no evidence and no theory showing it to be such a thing. There IS however much evidence showing that an electron is a particle, and that's because we measure it to be such a thing. To state that it is also a wave is nothing but disingenuous babble. If it's an electron then it's measured always as a particle.
So do you think the electron IS ever a wave? If so please state your evidence and/or theories which prove it to be such a thing.