Material is mostly vacuum:
"The diameter of the nucleus is in the range of 1.70 fm (1.70×10−15 m ...", from:
"The diameter of the nucleus is in the range of 1.70 fm (1.70×10−15 m ...", from:
This is not true in quantum physics. This is a big misunderstanding among many physics students that they live with for many years because they first learn about the atom using the planetary model of atom. In the planetary model the atom looks mostly empty. But this view of the atom becomes nonsense after learning QFT.
The space within an atom is filled with the wavefunctions of the electrons. If you still ask "but the electron is still going to be somewhere", I can only say that our intuition about classical physics fails in the quantum physics.
In quantum physics, an atom is not mostly vacuum. It is filled with wavefunctions of the electrons.
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
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.
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.
More obviously if you think about how easily neutrons interact compared to protons, neutrons routinely go right through people without noticing them at all because they aren't net charged so the coulomb interactions that we are familiar with in "normal" matter don't apply.
Also, I think that "point particles" are a rather illusory concept. More like, interactions between particles are highly localized when observed by a macroscopic classical observer.