Calculating the Volume of an 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]

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

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]

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

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]

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.

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]

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

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 ~ $${10}^{-18}m$$ 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]

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

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).

 

[vtakhist]

I don't get how that makes any sense that electron has 0 volume
As an approximation it can be thought of as having 0 volume, but as a physical fact that is just ridiculous.

If something has no spatial extensions,
then how can it exist if there is nothing in that space (otherwise it would have spatial extensions)?

from Wikipedia:

Matter - a general term for the substance of which all physical objects are made. A common way of defining matter is as anything that has mass and occupies volume.

Point Particle - is an idealized object heavily used in physics. Its defining feature is that it lacks spatial extension: being zero-dimensional, it does not take up space. A point particle is an appropriate representation of any object whose size, shape, and structure is irrelevant in a given context.


From this it follows that electron cannot be a point-particle and matter at the same time...so it can't exist if it is a point particle.

So as approximation just because we don't know, it can be treated as such, but saying that it actually is - makes no sense to me.

 

[Delta2]

Well the article in wikipedia refers to "A common way" of defining matter . I guess in the standard particle model the matter can consist of point particles (like electron) that have mass but occupy no volume.

The macroscopic view of matter as occuping volume probably comes from the fact that all these point particles are not in same place as brainstorm posted earlier on this page and that they move all the time, so a point particle moving spans a region of the 3D space that is a volume.

 

[vtakhist]

Things with no spatial extension still make no real physical sense (let's leave aside Wikipedia if you want).

Example1: you cannot properly integrate or sum over anything spatially if it has 0 extensions...

Example2: suppose you have a ball of finite size, now you take the ball to be a point ball with no spatial extensions, then if there is no more spatial extensions there is no more ball - since if there would be a ball it would exist and thus occupy some space - leading to a contradiction in assumption.

I have no problem saying things are infinitesimal (still occupying space but are so minute that this is taken as 0, but it is not 0)...but I do have problem with saying that things are actually have no spatial extensions whatsoever as being a real physical property and not a mere approximation.

 

[Delta2]

Well macroscopic objects like ball have volume and I already said why. So the macroscopic objects (and even microscopic ones like molecules and atoms) have volume (for example in the atom of hydrogen simplified the volume it occupies is the region of space where the proton and the electron are in and with the electron moving around the proton in a spherical region that is the 1s orbital). So you can integrate or do anything you like with the volume they occupy.

It is just the elementary particles like the electron that occupy no volume. Though this seems non physical it really might be the case. Think it otherwise, if something considered elementary and still occupied a volume then one could argue the he could split it to half the volume so that elementary particle is not elementary indeed ( however i am sure this is not the main reason we consider electron to be point particle in the standard model probably there is a more deep explanation).

 

[vtakhist]

It is totally not relevant what people call "elementary" or not...this is merely a convention and doesn't prove anything.

Electron is said to be a point particle just because all the measurements thus far have not established any particular size. As an approximation this is good.

If it actually has no spatial extension (point particle) - it makes no sense to talk about it since no spatial extension would mean it is not occupying any space, volume, length etc. Also, we do know that the mass if finite, so if the volume occupied by it is essentially 0 - the mass density is infinite?

Now if by point particle - we mean "infinitesimal" rather than volume and spatial extensions are 0, then this seems to address the problem.

 

[Delta2]

Now if by point particle - we mean "infinitesimal" rather than volume and spatial extensions are 0, then this seems to address the problem.

How does this adress the problem? Infinitesimal means arbitrary close to zero. So u mean that the electron volume is always small but non zero but can become as close to zero as we want depending on the phenomena we want to explain?

 

[K^2]

Electron is said to be a point particle just because all the measurements thus far have not established any particular size. As an approximation this is good.

Elementary particles are point-objects. Electron may not be elementary, but whatever it is made up of WILL be point-particles.

Tell me, what is the size of a photon? And why should electron be any different?

 

[Jasso]

Example1: you cannot properly integrate or sum over anything spatially if it has 0 extensions...

Of course you can, the integral of the Dirac Delta function (which has 0 width) in a region that contains it is 1.

Example2: suppose you have a ball of finite size, now you take the ball to be a point ball with no spatial extensions, then if there is no more spatial extensions there is no more ball - since if there would be a ball it would exist and thus occupy some space - leading to a contradiction in assumption.

Two issues:

1. You assume that objects must possesses a definite volume to exist; have you never heard of a black hole?

2. Macroscopic objects only take up space because of the distances between the constituent molecules/atoms/particles.

 

[Dr Lots-o'watts]

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

A volume has to be of something.

If you have 2 particles, that defines a distance. With 3, you have an area, and with x > 3, you can have a volume. That is one way to define a volume : the volume of the space between points or point-particles. So the volume of a basketball could be said to be the volume of space between its constituent particles. Of course, this doesn't allow for a volume to be defined for a single point, or a point-particle, such as an electron is believed to be.

However, we could also say that the volume of a basketball is the volume of space where it has an effect on other particles. For a basketball, this is pretty much the same volume as the one between its constituent particles.

In the same way, the volume of an electron could be said to be the volume of space where it has an effect on other particles. For the various systems I mentioned, this volume is different. Just find r where the coulomb force is significant in your system and calculate the volume (if it's spherical, which isn't necessarily that case within periodic matter).

 

[brainstorm]

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

Volume is typically conceived as a passive characteristic of a fixed entity. A volumeless point moving energetically in a closed pattern can produce the observed effect of fixed passive volume. It does this by exerting force on anything that comes in contact with it. This is why static electricity feels like a light fuzzy "blanket" over the surface of whatever is charged, I believe. If you attempt to compress anything with volume, the force that resists that of your compression is the force of the electrons interacting within the thing you are trying to compress. I'm sure there are many nuances as to the chemical and tensile structuring of the particles within a particular material that makes it more or less compressible, but the basic ability to resist compression comes from the force of electrons resisting changing their trajectory of motion during collisions with other electrons. Thus what appears as passive, fixed volume is actually caused by active electron force. This is my understanding, anyway.

edit: Another way to understand this would be to consider a ball that is deflated at sea level and then placed in a relative vacuum, where it appears to inflate. The inflation is the result of higher relative pressure of the air inside the ball versus the lower pressure outside. As the air particles inside the ball become more active in trying to escape and dissipate their energy into the surrounding low pressure air, they generate more volume in the ball with the same amount of air-mass. So it's not the mass or the volume of the particles that is relevant to the volume of the balloon; it's the energetic activity of the particles relative to their surroundings and the fact that they are contained/constrained within a bounded region.

 

[kunalkishore]

if electron is considered as a point sized particle...still it will be of some size in the order of some very very minor unit...(say 10^-100! or something like that)

ex:-consider a dot that u make on a paper...this dot will be of some size..when we look it through a microscope...isnt it?

 

[Drakkith]

In the same way, the volume of an electron could be said to be the volume of space where it has an effect on other particles. For the various systems I mentioned, this volume is different. Just find r where the coulomb force is significant in your system and calculate the volume (if it's spherical, which isn't necessarily that case within periodic matter).

Exactly. The "volume" of an electron could easily be said to be a sphere at X distance around the center of the electron. Make X whatever distance (radius) you want based on whatever strength of charge you want and call that the electron.

 

[Drakkith]

if electron is considered as a point sized particle...still it will be of some size in the order of some very very minor unit...(say 10^-100! or something like that)

ex:-consider a dot that u make on a paper...this dot will be of some size..when we look it through a microscope...isnt it?

Is an electron, or any particle for that matter, a hard sphere with a definite boundary? To my knowledge it is not. I can easily imagine an electron to be a "sphere of energy/mass", with the amount of energy/mass dropping off to near zero at near infinite range. It's kind of like an atmosphere of a star. It's there, but not very dense a large distance from the center of the star, but as you get closer the atmosphere gets denser and denser. Whatever distance from the center of the star you want define as the boundary of the actual star is up to you.

 

[sophiecentaur]

The problem here is that people are trying to be far too classical about this. For an item as small as an electron, you just can't say anything as definite as "how big is it?". For a start, depending on the context, you may have no idea where it actually is- for instance, when bound in an atom. How would you describe its sphere of influence when it has to be described in terms of a probability density function around a nucleus / solution to a wave equation? Heisenberg says that, if its momentum or energy state is known accurately then it could be just about anywhere so how does its "size" come into it?

 

[Antiphon]

How about saying it's at least the Planck length cubed? Isn't that the minimum meaningful volume of anything?

 

[sophiecentaur]

How about saying it's at least the Planck length cubed? Isn't that the minimum meaningful volume of anything?

How about saying that the size is not a meaningful question because the circumstances in which you try to measure it (which is what really counts) will totally dominate. And, remember, it's not 'really anything' - as with all modern Physics Concepts.

 

[dimension10]

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?

Well, a singularity can.

 

[sophiecentaur]

This thread is in danger of turning into a 'top trumps' game. The 'spec's of things like electrons don't really lend themselves to this sort of discussion.