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Oh, great, that's better, thanks. But you forgot to say how many rocks would fit into a football field?
by afew (afew(a in a circle)eurotrib_dot_com) on Fri Feb 22nd, 2008 at 09:03:31 AM EST
[ Parent ]
That was interesting. I thought I'd look up 'diameter of an electron' and found sizes between 10^-13 m and 10^-18 m.

The 'classical' radius is

Although all that really tells you is that you can't say how big an electron is, because unlike a rock it doesn't have hard edges. Instead it's defined by how much it bounces when you bang it with something else.

Curiously, football pitches also seem to suffer from quantum indeterminacy - very bad news for science journalists.

The official FIFA dimensions are '90-120m' wide and '45-90m' tall. Goal dimensions are defined as 7.32m x 2.44m, which presmably requires precision laser range-finding to make sure they're accurate to the nearest mm.

So - it's unlikely we'll ever know exactly how many electrons fit into a football pitch.

A bit unfortunate, that, but there it is.

by ThatBritGuy (thatbritguy (at) googlemail.com) on Fri Feb 22nd, 2008 at 09:36:32 AM EST
[ Parent ]
I have to live with uncertainty. It's killing me.
by afew (afew(a in a circle)eurotrib_dot_com) on Fri Feb 22nd, 2008 at 10:15:00 AM EST
[ Parent ]
You can say that the charge of the electron is contained in a sphere with radius less than 10 ^(-18)m and is assumed to be a point in the current theory.

However at LHC protons are used not electrons.
Protons have a diameter of about 10^(-15)m. Of course not the protons, but the quarks and at LHC even mainly the gluons are colliding.

For the non-experts, the following picture is an illustration of a proton by the Oxford Hera group's website.

The dots are quarks. In a proton quarks minus antiquarks net 3 quarks. The springs represent gluons. The lower energy you count the more gluons are there. These are the "force particles" of the strong interaction, which holds as well nuclei together, and have the interesting property that they carry as well strong charge.

The best known "force particle" is the photon, which is the carrier of the electromagnetic interaction. Others are gravitons (not yet directly observed, but who doubts they exist), and the W (Z) bosons, the carrier of the weak interaction, which are the only force particles known which have mass.

Der Amerikaner ist die Orchidee unter den Menschen
Volker Pispers

by Martin (weiser.mensch(at)googlemail.com) on Fri Feb 22nd, 2008 at 10:17:12 AM EST
[ Parent ]
The radius of a proton is a more meaningful quantity than the radius of an electron, because as far as we know the electron is pointlike (no internal degrees of freedom) but a quark is a composite particle containing three quarks and so in principle one could assign it a radius just like the hydrogen atom - a composite particle of a proton and an electron can be assigned a radius by studying the electron wavefunction for its ground state.

Then again, the "radius" of a wavefunction, be it the electron orbital in an atom or the wf of a quark in the proton, is only meaningful as an order of magnitude anyway.

We have met the enemy, and he is us — Pogo

by Carrie (migeru at eurotrib dot com) on Fri Feb 22nd, 2008 at 03:22:25 PM EST
[ Parent ]
You are a theory guy, right? ;-)
10^(-18)m is experimentally tested, point is what the theory says.

But more important you have a typo
"but a quark is a composite particle containing three quarks", should be proton is a composite particle...

Der Amerikaner ist die Orchidee unter den Menschen
Volker Pispers

by Martin (weiser.mensch(at)googlemail.com) on Fri Feb 22nd, 2008 at 04:02:56 PM EST
[ Parent ]
In a previous life I was a theory guy, yes, though I took my graduate Standard Model courses from a pretty good phenomenologist.

I suppose I could find it in the particle data booklet, but can you outline the experiment that tests the electron radius?

We have met the enemy, and he is us — Pogo

by Carrie (migeru at eurotrib dot com) on Fri Feb 22nd, 2008 at 04:51:20 PM EST
[ Parent ]
Well, how do we know that the proton has a fm? When hitting it with a charged particle with a Compton wavelength in the order of 1 fm in a scatter experiment, we start to see a formfactor, e.g. the particle doesn't see the full charge any more.
LEP II had about 100 GeV/c^2 per electron, therefore a Compton wavelength of about 10^(-17)m, and there was not the slightest sign of substructure, we still see absolutely the full structure and one would likely expect already small signs of a formfactor with a somewhat bigger wavelength than the electron size.

I don't know what measurement exactly provides the best measurement, could be a precision measurement of the B sector or whatever, but that's it pretty much.

Der Amerikaner ist die Orchidee unter den Menschen
Volker Pispers

by Martin (weiser.mensch(at)googlemail.com) on Fri Feb 22nd, 2008 at 05:17:09 PM EST
[ Parent ]
There's more than one LEP? that's scary ;-)

Any idiot can face a crisis - it's day to day living that wears you out.
by ceebs (ceebs (at) eurotrib (dot) com) on Fri Feb 22nd, 2008 at 05:32:24 PM EST
[ Parent ]
The electron is, as far as we can tell, a "point" particle, meaning that it has no internal degrees of freedom: all its degrees of freedom have to do with its relation with the surrounding space(-time).

The classical radius of the electron is the radius of a sphere such as the energy of the electric field outside it matches the observed rest mass of the electron. If you assume a "classical" electron is truly pointlike you get an infinite energy for its electric field.

The funny thing about quantum field theory is that, since the electron is pointlike (see first paragraph) you need to "renormalize" the self-interaction of the electron (i.e., the interaction of the electron with its own electric field) and renormalization methods involve a "cutoff" (effectively, a mass or a radius cutoff - see second paragraph). You then ger "running coupling coefficients" which means that the "bare mass" and the "bare charge" of the electron vary with the "cutoff".

We have met the enemy, and he is us — Pogo

by Carrie (migeru at eurotrib dot com) on Fri Feb 22nd, 2008 at 03:18:33 PM EST
[ Parent ]

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