people say this casually... and fail to define what a wave-function is physically.
It sounds like a non-sense answer.
if there is matter there, in the form of a 'wave function', what is the matter of a 'wave function' (other than just the electron zipping about)?
no: a wave function is a mathematical construct we use to predict where an electron might appear... (well, not exactly the wave function, but we get the probability of an electron's appearance by squaring the wave function).
A wave function (probably), doesn't 'physically' exist. it's just a useful model to predict probabilities...
waves exist only in a medium of expressive material - if that material is a single electron, there isn't magically more material there once we use a wave function to predict it's location - it's still only one electron - it's position predicted by the square of the wave function - but that doesn't mean the wave function is a physical entity.
And it's not like the electron is 'going faster than light' and 'blurring frames in reality'... it's just the electron there - the squaring wavefunction is just a way to predict it's location: just because it (seems to) works doesn't mean it physically exists.
but if it DOES exist physically (in a concrete way) - I would love an explanation or link to that proof - as that would be news to me.
fundamentally this might just be a semantics issue on the word physical
What you're asking for doesn't currently exist. At least not any proven ones. There's a dozen new philosophical interpretations of quantum mechanics every year but they usually make no new predictions, so there is no way to test if the interpretation is correct.
Most (all?*) interpretations only differ in defining the "wavefunction collapse" and what happens before it. But since measuring anything involves collapsing the wavefunction, it's impossible to measure what happens before that.
We do know, from real-world experiments, that particles cannot actually be moving point-like objects. The most famous example is the double slit experiment where a single particle can cause wavelike interference with itself.
But also we know it isn't exactly a classical wave. We can only measure it as a single point, and it arrives in discrete events, not a continuous transfer of energy like a wave.
So "wavefunction" and the rest of QM lingo is what we have. We don't fully know what those are, but we also know that being just a point or wave in the style of classical physics cannot be correct.
* If an interpretation does make a new prediction that is measurable, I'm not sure if it's considered just an interpretation anymore.
Note that you are demanding something impossible: you are demanding a "physical" explanation, but what you seem mean by "physical" is "something that I can intuitively understand with my preconceived notions". But nature doesn't care whether the reality fits your intuition or not!
The wave-function – a model that fits the data – is defined mathematically, and by Occam's razor, anything "fluff" added to it that makes it "easier to grok", makes it _further_ away from an actual explanation of reality.
It sounds like a non-sense answer.
if there is matter there, in the form of a 'wave function', what is the matter of a 'wave function' (other than just the electron zipping about)?
no: a wave function is a mathematical construct we use to predict where an electron might appear... (well, not exactly the wave function, but we get the probability of an electron's appearance by squaring the wave function).
A wave function (probably), doesn't 'physically' exist. it's just a useful model to predict probabilities...
waves exist only in a medium of expressive material - if that material is a single electron, there isn't magically more material there once we use a wave function to predict it's location - it's still only one electron - it's position predicted by the square of the wave function - but that doesn't mean the wave function is a physical entity.
And it's not like the electron is 'going faster than light' and 'blurring frames in reality'... it's just the electron there - the squaring wavefunction is just a way to predict it's location: just because it (seems to) works doesn't mean it physically exists.
but if it DOES exist physically (in a concrete way) - I would love an explanation or link to that proof - as that would be news to me.
fundamentally this might just be a semantics issue on the word physical