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## What exactly is an electron?

 Quote by Vanadium 50 There is no prediction for the charge radius of the electron. There are experimental limits suggesting that any charge radius must be smaller than some number, but the number that A. Neumaier posted is neither a prediction nor a measurement.
I haven't seen the paper, but according to the abstract: ''indicate the validity of the SM down to the distance of order ~10^{-17} cm and the electron charge radius of ~ 10^{-16} cm.''
Thus there seems to have been a comparison between experiment and a prediction, though the number given is maybe only a bound.

I haven't found a calculation that I could have checked, But in principle, a prediction is possible: In his book

S. Weinberg,
The quantum theory of fields, Vol. I,
Cambridge University Press, 1995,

Weinberg defines and explicitly computes in (11.3.33) a formula for the
charge radius of a physical electron. But his formula is not
fully satisfying since it is not fully renormalized (infrared
divergence: the expression contains a fictitious photon mass,
and diverges if this goes to zero, as infrared corrections from soft
review article

M.I. Eides, H. Grotch, and V.A. Shelyuto,
Theory of Light Hydrogenlike Atoms,
Phys. Rep. 342 (2001) 63-261.
http://arxiv.org/pdf/hep-ph/0002158

where the authors says:
''According to QED an electron continuously emits and absorbs virtual
photons (see the leading order diagram in Fig. 8) and as a result its
pointlike''. Then they give without proof the explicit formula (28)
for the charge radius, depending logarithmically on the charge of the
central field in which the electron moves.

But according to (7.12) in Phys. Rev. D 62, 113012 (2000),
the charge radius of neutrinos, another pointlike particle, computed
from the standard model to 1 loop order, is in the range of
4...6 10^-14 cm for the three neutrino species.

Mentor
 Quote by A. Neumaier I haven't seen the paper
Then maybe you should. You brought it up.

Recognitions:
 Quote by Vanadium 50 Then maybe you should. You brought it up.
I don't know how to get it.
 Mentor Normally when someone references a book or article that they haven't read, that pretty much ends the discussion. However, I don't want this thread to end on such a misleading note. How does one quantify substructure? One can model an electron as a uniformly charged sphere of radius r. The sensitivity of an experiment is R if it can distinguish between a sphere of radius R and one of radius r, with r << R, but not any smaller than R. (In the interest of full disclosure, hard spheres have technical difficulties, so Today we know that for an electron r < 10-18 or a few 10-19 meters. These numbers come from both precision measurements at low energy and a search for deviations from a point-like geometry in high energy scattering. Note that this isn't saying that an electron is a point; it's saying that it appears pointlike, but that we cannot resolve a distance smaller than about 10-18 meters. So where does this 10-16 number come from? That's the distance at which vacuum polarization becomes important and thus where the electric field starts to depart from a ~1/r potential. This happens for all charged objects: electrons, muons, quarks It would be profoundly misleading to attribute this to electron substructure because a) it is a property of every single charged particle, not just the electron and b) happens whether the electron is fundamental or composite.

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 Quote by Vanadium 50 Normally when someone references a book or article that they haven't read, that pretty much ends the discussion. However, I don't want this thread to end on such a misleading note.
I had given references that I read and understood (Weinberg Chapter 11.3, with an explicit formula for the renormalized charge radius, though in terms of a tiny photon mass, because this kind of computations have IR divergences). Only in response to the query for an explicit value, I referred to something I couldn't access but seemed to give such a value.

 Quote by Vanadium 50 How does one quantify substructure? One can model an electron as a uniformly charged sphere of radius r. The sensitivity of an experiment is R if it can distinguish between a sphere of radius R and one of radius r, with r << R, but not any smaller than R.
I wasn't speaking of substructure in the sense of being composite, but of not having the properties of a point.
 Quote by A. Neumaier The electron is an elementary particle, hence not composed of anything but itself. But it is not a point - only pointlike (which means, the formal, unobservable, bare electron in the defining action is a point). Due to radiative corrections stemming from the renormalization procedure for relativistic quantum field theories, an observable, renormalized electron has a positive charge radius (though far too small to be probed experimentally with current methods).
This is the case for purely theoretical reasons, a direct consequence of QED, which is generally acknowledged to be reliable in this regime. (Corrections from the standard model would be tiny and not alter the general fact.)

 Quote by Vanadium 50 So where does this 10-16 number come from? That's the distance at which vacuum polarization becomes important and thus where the electric field starts to depart from a ~1/r potential. This happens for all charged objects: electrons, muons, quarks It would be profoundly misleading to attribute this to electron substructure because a) it is a property of every single charged particle, not just the electron and b) happens whether the electron is fundamental or composite.
I didn't attribute it to electron substructure but to Weinberg's discussion in his QFT book. (One might attribute it to virtual substructure the physical electron being a composite of a bare electron and a cloud of bare virtual photons, but I don't like this sort of imagery.)

Recognitions:
 Quote by Vanadium 50 One can model an electron as a uniformly charged sphere of radius r. The sensitivity of an experiment is R if it can distinguish between a sphere of radius R and one of radius r, with r << R, but not any smaller than R. (In the interest of full disclosure, hard spheres have technical difficulties, so Today we know that for an electron r < 10-18 or a few 10-19 meters. These numbers come from both precision measurements at low energy and a search for deviations from a point-like geometry in high energy scattering. Note that this isn't saying that an electron is a point; it's saying that it appears pointlike, but that we cannot resolve a distance smaller than about 10-18 meters.
Let me complement your experimental view with the theoretical side of the matter.

The deviations from pointlikeness are usually described by means of
form factors that would be constant for a point particle but become
momentum-dependent for particles in general.

The form factors contain everything that can be observed
about single particles in an electromagnetic field.

http://en.wikipedia.org/wiki/Electric_form_factor :
''The electric form factor is the Fourier transform of electric
charge distribution in space.''

http://en.wikipedia.org/wiki/Magnetic_form_factor :
''a magnetic form factor is the Fourier transform of an electric
current distribution in space.''
In particular, the charge radius is defined as the number r such that
the electric form factor has an expansion of the form

$$F_1(q^2) = 1-(r^2/6) q^2$$ if $$r^2q^2<<1$$.

(Units are such that c=1 and hbar=1.) This definition is motivated
by the fact that the average over exp(i q dot x) over a spherical shell
of radius r has this asymptotic behavior.
See Formula (11.3.32) in

S. Weinberg,
The quantum theory of fields, Vol. I,
Cambridge University Press, 1995.

QED (which treats the electron as pointlike in the usual sense of the
word - that it appears as a fundamental field in the Lagrangian) imply
a positive value for the charge radius of the electron. Indeed, this
is Weinberg's conclusion from his calculations in Section 11.3,
together with an estimate of infrared effects taken from (14.3.1).

 Quote by CF.Gauss What exactly is an electron?

The electron is a elementary subatomic particle with a negative elementary electric charge. It has no known components or substructure.

Observation of a single electron in a Penning trap shows the upper limit of the particle's radius is 10^−22 meters.
$$r_e \leq 10^{-22} \; \text{m}$$

I request to make a recommendation for the Physics Forums Science Advisers to simply cite and reference a Wikipedia webpage for layman original poster (OP) subject questions, instead of referencing high level physics science papers, in order to avoid a lot of confusion and hyperbole.

Reference:
Electron - Wikipedia
 electron is electron only. we are still investigating that elementary "thing". we know some of it's properties, ie. particle property, wave property, charge, mass etc. we dont know what exactly it is, only can measure some of it's characteristics, thats all
 Well said lordsandman. If we ever come to understand what an electron really is then we won't need high energy machines anymore.

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Gold Member
 Quote by ailog Well said lordsandman. If we ever come to understand what an electron really is then we won't need high energy machines anymore.
How do you know we don't understand what an electron really is?
 Mentor How do you define "what an electron really is", without just describing its measured properties? And even worse: How do you test this, if you cannot use any measurement by construction?
 To Drakkith Well, it depends on what understand means to those studying the issue. I suppose the words "understand" and "really" should banned from the world of physics.

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Gold Member
 Quote by ailog To Drakkith Well, it depends on what understand means to those studying the issue. I suppose the words "understand" and "really" should banned from the world of physics.
I think people should understand that we can't even know if our knowledge about something is complete. So making statements like "when we really understand" is 100% meaningless.

Mentor
 Quote by ailog If we ever come to understand what an electron really is
How will we know when we have reached that point?

 Quote by Drakkith I think people should understand that we can't even know if our knowledge about something is complete. So making statements like "when we really understand" is 100% meaningless.
I am not sure if you are quoting me but what I said was "If we ever come to understand what an electron really is". There's a big giant if in the statement. I don't believe we ever will and not just for the electron. The universe is too complex for our order of intelligence.

 Quote by jtbell How will we know when we have reached that point?
If we are smart enough we will admit that there will always be something to learn and we will never reach that point. But I left the possibility open with an if statement. Now if I can figure out a method to create an electron out of a vacuum at my garage workbench then I'm getting closer.
 If the universe is governed by a number of laws, we can learn these laws, no matter how complex they are. Being so distant doesn't mean we will never reach. About the OP's question, I believe he is asking about it's volume and shape, and other physical properties usually observed by eyes.

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