Re: electron, proton size

[John Denker <jsd@MONMOUTH.COM>]

At 09:59 AM 8/14/99 -0400, Herbert H Gottlieb wrote:
> The mass of the proton is about 1837 that of the electron

OK.

> and their charges are opposite, but equal in magnitude.
> What is the relation of the electron size compared with
> that of the proton?  How was this determined?

Here are a few of the many ways to answer that question.

Let's start with the electron.

a) If by "size" you mean the electron-electron scattering cross section,
then the size is infinite.  Electromagnetism is the quintessential
long-range force.

However, this is not what people usually mean by size.  The moon attracts
asteroids via an infinite-range gravitational force, but we don't say that
the moon is infinite sized.  We typically subtract off the long-range force
and use the word "size" to refer to some short-range force that turns on
when the test particle "hits" the main object.

But we should not forget that the long-range force is there.

b) If you are looking for a short-range force that tells you something
about the internal structure of the electron, then the size is zero.
Nobody AFAIK has ever managed to whack an electron hard enough to see any
internal structure, or any force other than the long-range electromagnetic
force.

c) There is AFAIK no clear theoretical reason to expect electrons to have
internal structure.

Superstring theory may change this, but that theory is in a pretty murky
state right now, and very far from any experimental test.

d) There is the Compton wavelength, but that has more to do with virtual
electron/positron pairs than with real electrons.

e) There is the classical electron radius as discussed in Feynman II-28,
but experimental evidence shows that nothing special happens at this
radius;  it is certainly not like an asteroid hitting the surface of the moon.

BOTTOM LINE:  for all practical purposes I can think of, you can think of
the electron as having *zero* core size, surrounded by the long-range EM field.

================

Now for the proton, the story is quite a bit different:

a) As before, the proton-proton scattering length is technically infinite,
because of the EM field.  But people usually subtract that off.

b) At short range, there is the strong nuclear force.  This is mediated by
exchange of pions, and its range is set by the mass (i.e. Compton
wavelength) of the pions.

c) So you can think of the proton as a hard core surrounded by a cloud of
virtual pions (and further surrounded by the EM field).  For many
experiments, it is the cloud of pions that sets the "size".

c') If you look closer, you find that there is tons of additional internal
structure.  You see quarks held together by virtual gluons.  The gluons are
really massive, so you their range is really short (and there are other
range-shortening factors at work as well).

d) There is of course the Compton wavelength of the proton, but that's
probably not the answer you were looking for.

e) You can play mass-of-the-field-energy games for protons as well.

BOTTOM LINE:  For most purposes, your students will be safe thinking of the
proton as a bundle of strong force about a fm on a side, surrounded by the
long-range EM force.

Does that come close to answering your question?