If your argument is simply "quantum field theory is right", well, great. Quantum field theory is right, as far as anyone can tell! Glad you agree.
Yes I do. Remember it isn't me who goes round saying Einstein was wrong or Feynman was wrong. The issue is, as ever, one of interpretation. It's quantum
field theory, the electron
is field. It isn't some little billiard-ball thing which has a field.
But you think we shouldn't use the word "point particle" when talking about a wavefunction?
Yes. Point particles are a mathematical abstraction. There is no place for them in contemporary physics.
There are two different totally phenomena with separate scales here: (a) the length scale associated with internal degrees-of-freedom of all objects of this type vs. (b) the spatial extent of the object's wavefunction in a given experiment.
Never mind some given experiment. Think of an electron just sitting there in space. The electron is just field. And there is no place where that field stops.
All hydrogen atoms have internal stuff going on a scale of 1A. All lead nuclei have internal structure spread over 8fm. All protons have internal structure spread over 1fm. All C60 buckyballs have internal structure spread over 10nm. A baseball has internal structure over 10cm. This is all visible in experiments. This is the scale you see in scattering experiments.
Not a problem. Nor is proton diffraction a problem. Nor buckyball diffraction.
You can prepare an atomic hydrogen beam in which the particle positions are uncertain on a scale of 1cm. Or 1mm. Or 1A. Depends on the experiment. You can prepare a proton beam where the wavefunction diffracts through two slits 100um apart. Or 1um. Or 1nm. Depends on the experiment. It's a totally different phenomenon than the scale mentioned in the previous paragraph.
You really do have a deep-rooted point-particle concept don't you? A hydrogen atom is made up of an electron and a proton. Both are just field. And there is no place where that field stops.
On the first observable: scattering experiments cannot find a spatial scale associated with electrons qua electrons. No matter how hard we look. This means there is no such scale down to 10^-18m.
It's like sticking a barge pole into a whirlpool and complaining because you can't feel the billiard ball, then asserting that the billiard ball must be really small.
The standard term for the former quantity is "the size of the particle". If I say "the size of a buckyball is 10nm", I'm referring to the former quantity. You cannot rebut this by pointing out a buckyball diffraction experiment that used 100nm slits---that's referring to the latter quantity.
The standard term will not help your understanding. You have to think waves. For example, think of a seismic wave where the Earth moves back and forth by one metre. How big is it? Not one metre. If this seismic wave rippled across the surface of the Earth between A and B it doesn't only affect the properties on the AB line. It takes many paths. You could plot its size with a large array of detectors and say it extends until it is no longer detectable. Only you can detect it from the other side of the Earth.
I will continue to say "electrons are pointlike", and I'm always referring to the former quantity. Electrons are pointlike in the same sense that hydrogen atoms are 1A wide and protons are 1fm wide. Electrons are wavelike in the same uncontroversial sense that everything is wavelike.
Ben, watch my lips and learn this well:
electrons aren't pointlike. And neither are hurricanes.