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Re: point particles

Consider the size of the electron first.

There is no experimental evidence yet that implies that
electrons are not points in the mathemaical sense. Present
scattering experiments limit the size of an electron to be
less than or equal to a given number. If you shoot 2
electrons at each other at relativistic energies, they
scatter from each other as if they were point objects.
Because the dominant force responsible for scattering is
the electrical force or the Coulomb force, it is also like
scattering from a point charge. Now the higher you go in
electron beam energy, the smaller the limit you can put on
the size of the electron. Presently it is about 1.0xE-18
m. This corresponds to about a beam energy of 200 GeV or
2.xE+11 eV in the center of mass of the two electrons. If
you probe deep enough by using higher energy electron
beams, eventually you might expect to find a smaller
limit. This is because like charges repel and can not
exist in exactly the same spot. However, we don't even
know if the electron has a distribution or not. What you
measure is the limit of the size of the charge
distribution and that is what we refer to as the size of
the electron.

Because the electron has spin or is a spinning charge it
also has a magnetic moment. This would also contribute to
its scattering and is refered to as transverse scattering.
This would also limit the size of the electron due to its
spinning motion.

If the electron had a slight displacement of its center of
mass to its center of charge, it would have what is called
an electric dipole moment. It also would contribute to
scattering and limit its size due to this small
difference. I don't know what this limit gives.

In any scattering experiment of 2 electrons all the above
terms would contribute. What you measure is a combination
of all terms which limits the size of the electron. I
actually do not know the most up to date limit is but it
is close to what I gave above.

Since the electron has mass, the gravitational scattering
between two electrons could be used to determine the limit
on the size of the electron's mass. However, because the
gravitational force is so weak, you can not measure the
scattering due to it because the scattering is overwhelmed
by the electrical force.

Therefore, the size of the electron or any object is
directly related to the way in which you scatter from the
electron or object.

Quarks can not be isolated and there are different kinds
with different masses. You can not scatter an isolated
quark from another one like you can with an electron.
Therefore, the fact that we say quarks are pointlike is
really based on the standard model and not experimental
data the way the electron is.

This is probably more than you ever wanted hear.

Richard Lindgren








On Tue, 20 Jan 2004 19:42:05 -0800
John Denker <jsd@AV8N.COM> wrote:
Quoting cliff parker <cparker@CHARTER.NET>:

What do you mean by internal structure? I imagine a
marble or BB as an
object with no internal structure. Meaning homogeneous
material through and
through. All marble and nothing else.

The way particle jockeys use the term, especially in this
context, "structured" is the antonym of "pointlike".
Internal structure means about the same as structure.

In this context, a marble or a BB clearly has structure,
the sort of structure you'd see in a scattering
experiment.
In the vicinity of a marble, there is trivial (i.e.
vacuum)
dielectric constant outside a certain radius R, and a
conspicuously non-trivial dielectric constant inside that
radius. If you probe it with something having a
wavelength
on the order of R, you are definitely going to notice
that
it's not pointlike.

An electron, in contrast, appears to be pointlike
according
to all experiments to date. It's smaller than a radio
wave.
It's smaller than a microwave. It's smaller than a light
wave.
It's smaller than a gamma. .... You get the idea.

Maybe somebody will see the structure of the electron
tomorrow. Maybe it's a string. I dunno. But I wouldn't
wager a lot on its being absolutely totally pointlike.

Are
you talking about things like charge distribution
appearing to originate
from one point. No tiny "tide" effects, that sort of
thing? Therefore no
implied size?

Tides and internal "mechanical" resonances are a more
advanced
subject. You can hypothesize a marble that is "all
marble and
nothing else" but a real marble will have phonons and
other
excitations running around inside it. Almost anything
you can
imagine that has nonzero size will have an "inside" and
then
somebody is going to ask "what's inside".

A "particle" consisting of a void in an otherwise perfect
piece of clear glass may not have "internal" structure in
the strictest sense, but it will still have an easily
detectable size and (if you look closer) will be subject
to mechanical distortions, so it will act like a particle
with all kinds of structure.