>It's probably more accurate to say "size" has no meaning at that scale
Not at all. Size has unambiguous meaning down to the Planck scale (10^-35 meters) and electrons simply haven't been probed at scales smaller than 10^-22 meters. They could very well have heretofore-undetected structure (e.g. preon models) on the scales of 10^-20 while still have fifteen orders of magnitude (about the relative span between an atom and the radius of the earth) over which distances are perfectly sensible.
Likewise, before the deep inelastic scattering experiments of the 60's, physicist had no direct evidence that neutrons and protons had any internal structure. All they could say is "we know that if they have internal structure, it's smaller than this length scale".
[FYI: The Planck scale is (arguably!) where the notion of size becomes murky because quantum fluctuations in the background spacetime (against which the sizes of things are measured) become substantial. Of course, no one has ever seen (even indirect) evidence of a quantum fluctuation in spacetime. And, as is well known, appling quantum mechanics to gravity and spacetime is full of difficulties. But most physicists believe there are such quantum effects because it seems damn near impossible to reconcile a classical spacetime with quantum everything else.]
Size of what, then? Its not a particle. Having internal structure doesn't mean volume makes sense. You're right that distances do make sense, and he probably meant the electron has no known internal structure. But I don't know how you'd talk about size unless you mean a zone of probability of where it is.
It is a particle. With a wavefunction. HN isn't the best place to teach quantum mechanics, but suffice it to say that the notion of spatial wavefunction spread is completely separate from the idea of particle being point-like vs. having internal structure of significant volume.
Comments
>It's probably more accurate to say "size" has no meaning at that scale
Not at all. Size has unambiguous meaning down to the Planck scale (10^-35 meters) and electrons simply haven't been probed at scales smaller than 10^-22 meters. They could very well have heretofore-undetected structure (e.g. preon models) on the scales of 10^-20 while still have fifteen orders of magnitude (about the relative span between an atom and the radius of the earth) over which distances are perfectly sensible.
Likewise, before the deep inelastic scattering experiments of the 60's, physicist had no direct evidence that neutrons and protons had any internal structure. All they could say is "we know that if they have internal structure, it's smaller than this length scale".
[FYI: The Planck scale is (arguably!) where the notion of size becomes murky because quantum fluctuations in the background spacetime (against which the sizes of things are measured) become substantial. Of course, no one has ever seen (even indirect) evidence of a quantum fluctuation in spacetime. And, as is well known, appling quantum mechanics to gravity and spacetime is full of difficulties. But most physicists believe there are such quantum effects because it seems damn near impossible to reconcile a classical spacetime with quantum everything else.]
Size of what, then? Its not a particle. Having internal structure doesn't mean volume makes sense. You're right that distances do make sense, and he probably meant the electron has no known internal structure. But I don't know how you'd talk about size unless you mean a zone of probability of where it is.
It is a particle. With a wavefunction. HN isn't the best place to teach quantum mechanics, but suffice it to say that the notion of spatial wavefunction spread is completely separate from the idea of particle being point-like vs. having internal structure of significant volume.
It is a particle, just because it has a wavelength doesn't mean it's not a particle.
An elephant has a wavelength it's just that it's rather small compared to the elephant
Indeed. See De Broglie's equations.
http://en.wikipedia.org/wiki/Matter_wave