Volume of electron

FizixFreak

has the volume of an electron ever been calculated if yes than what is its value?

arildno

At the length scales of the electron, I don't think volume is a meaningful quantity any longer.

Perhaps a professional physicist could give you a more satisfactory answer, but I doubt it.

Dr Lots-o'watts

A volume can be defined for the space where it's probably located. But this depends on its state i.e. you have to specify which electron your are talking about : one that is free, one that is in a field, one that is bounded to an atom, one that is inside a solide etc.

jnorman

the electron is a point particle. it has zero volume.

Bob S

The bare electron is believed to be a point particle, but the bare electron is "shielded" by a cloud of virtual electron-positron pairs (vacuum polarization) that reduces the observed charge at large distances (low momentum transfers). This correction was first calculated by Uehling in 1935 (Phys Rev 48 55). The Uehling correction (around an atomic nucleus) is an important contribution to atomic energy levels in pionic and muonic atoms, which penetrate the virtual electron-positron cloud..

Bob S

arildno

So, mathematically, the electron can be seen as a type of singularity, or rupture, that generates a smoothing effect around it called the Uehling correction?

Delta²

Classicaly there is http://en.wikipedia.org/wiki/Electron_radius where we picture the electron occupying a volume of a sphere with that radius.

jnorman

and from the main wikipedia page on "electron" - "it is defined or assumed to be a point particle with a point charge and no spatial extent."

FizixFreak

correct me if i m wrong but mathematically having zero volume would mean that the electron occupies no space even though it has mass.
can anything has zero volume without being massless?

sophiecentaur

Doesn't the HUP and the de Broglie wavelength come in here?
'Having a volume' relates to 'where you are likely to be found or detected' so wouldn't the effective volume of a particle relate to how well specified its momentum was?

ZapperZ

There's several different level of confusion here.

A ball has a volume AND a position. Typically, the position is the location of the center of mass or center of volume. Several people here have confused the spread in location as being the volume of the object. This is incorrect. The HUP, for example, deals with the LOCATION of the object, and not just for an electron (point particle), but also something with a "volume", such as a proton, neutron, Buckyball, etc.

To answer the OP, to the best of our knowledge now, an electron as no volume. Theories that have been shown to have a high degree of validity, such as QED, treats electrons as point particles, as has been mentioned. Now, whether later on we will discover that the electron has some sort of a volume, that's a matter of speculation. But if you want to know what we do know now as far as our state of knowledge, that is it.

The issue of whether something with no volume can have mass is a different bag of worms. If you buy into the Higgs mechanism, then this will no longer be an issue. This is because essentially all elementary particles are massless (yes, even the ones with "volumes"). It is how they interact with the Higgs that endows them with masses (ignoring the fact that there are indications that the quarks masses may not be entirely due to the Higgs). One can easily see how this could occur because there are many systems in which the electron acquire large masses, some time even up to 200 to 400 times its bare mass (see the heavy fermionic compounds). So having a "volume" is not a requisite to having a mass.

Zz.

arildno

Thank you, ZapperZ, for providing a clarification of the different issues clumped together here!

Should we then, for now, rather than worrying about the electron's "volume" be more interested in what particular, observable effects predominate at different distances from the point particle?

Chartering the local topography, so to speak, around the electron?

FizixFreak

how do these different situations you describe change the answer to my question???

Delta²

Noob question: If all the elementary particles are point particles with no volume, then how the macroscopic objects have volume?

arildno

By being empty space brim full of physical interactions between the particles.
That will distinguish the region from other regions of empty space, labelling it as the volume of the macroscopic object

Now, don't take my word for this, I merely suggest a feasible way of thinking around this.
It's most likely wrong, in many details.

For example, SOME fundamental particles might have volume, whereas others don't.

graphene

Many experimental observations are explained to a good level of accuracy by theories that assume the electron (& the nucleus too) to be point-particles.

For electrons, I am not really sure of which experiments point towards the finite size of electrons, but I've heard of particle physicists estimating orders of magnitude ~ [tex]{10}^{-18}m[/tex] for the 'diameter' of the electron. Atomic physicists are working towards finding the electric dipole moment (i.e charge distribution) of the electron, which sounds very interesting to me. :)

brainstorm

If points have no volume, how can two of them define a one-dimensional line, or three of them define a two-dimensional plane or three-dimensional space?

Answer: by not all being in the same location.

Translated to electrons/particles: energy creates momentum and motion, and thereby can generate volume even if the constituent particles do not themselves have volume - as long as they have energy/momentum and the capacity to interact with others (which can be assumed by the fact that they have momentum/energy, I believe).