# The size of an electron

1. Nov 4, 2006

### lightarrow

Is it possible to define in some way, theoretically or experimentally, a size for an electron?

2. Nov 4, 2006

### vanesch

Staff Emeritus
It is of course possible to ask that question, but then, one needs to define exactly what one understands by "electron". Evident as it may seem, when thinking through it, you'll see that the concept is only evident in certain situations where in fact the question of size doesn't make much sense, because, by assumption, it's a pointlike particle.

On the other hand, you may assume "electron" to be a theoretical concept within a certain theory (+ interpretation). Well, then it is simply the theory at hand that will define what is its size.

In non-relativistic QM, an electron is a "thing" with 3 space degrees of freedom: x,y and z, plus a discrete spin degree of freedom. As such, it is assumed to be a point in Euclidean space, and hence its size is assumed to be 0. In how much this theoretical (idealised) model corresponds to reality is of course left in the middle.

In QFT, the "electron" can be seen as excited states of a field. It has then a rather abstract notion, and I'm not sure that size has any relevance to it.

In speculative theories such as string theory, in as much as there is such a thing as an electron :-), it has a certain geometrical structure, and as such, one could, in this case, talk about its size.

When experimentally determining the "upper size boundary" of an electron, then this comes down to comparing experimental results with certain theoretical models, which assume a finite size of the electron, and falsifying models which have an electron size above a certain value.

I concur with Zapper as not to take the extension of the wave function describing the electron as its "size". The wave function is not the electron itself, but only describes its kinematical state according to quantum theory. Its extension in "space" only describes in as how much, according to quantum theory, we have to consider superpositions of different possible positions of the electron. Although one shouldn't push the equivalence too far, taking the wavefunction as a measure of the size of the electron would be similar to taking as the size of a truck, the uncertainty that one has in its position on the highway (say, if the truck has been coming by certain check points, and from there, we calculate a certain probability function of its current position). If we have a high uncertainty on the truck's position (say, 20 km), nobody in his right mind would now say that the truck's size is 20 km.

3. Nov 4, 2006

### Staff: Mentor

How would one define the size of a particle experimentally?

You might say, it's the size of the smallest hole that the particle can pass through. But as far as we know, an electron can diffract through any size aperture. In fact, we don't even need an aperture at all! (quantum-mechanical tunneling)

You might say, it's the closest distance that you can aim one (moving) particle at another one and still have them miss (not collide). But one electron can "bounce" off another via their electrical repulsion, regardless of the distance of closest approach, as far as we know. The predictions of QED for the results of electron-electron and electron-positron scattering, assuming pointlike particles, have been verified up to the highest achievable energies, corresponding to tiny approach distances (in a classical sense). Believe me, it would be big news if any discrepancies appeared!

Got any other ideas?

4. Nov 4, 2006

### lightarrow

At which energies are those experiment performed? Very high. From De Broglie relation it comes that their associated wavelenghts are extremely small, so it's not such a surprise to me that they behave as point-like. Having said this doesn't correspond to have said that electron's size = wavelenght; I'm wondering about a possible relation between the two things.

By the way, I'm not even saying that this (if meaningful) concept of "electron's size" is related to "breadth" only or "lenght" only or whatever else.

If we were talking about real wavepackets, everything would have been much more clear, but we know that it's not the case, so all I can do is to imagine a sort of analogy.

Last edited: Nov 4, 2006
5. Nov 4, 2006

### tehno

Not exactly,but there is thing in physics called "classical electron radius".
Do a Google for it to see what it means and how it is derived.

Last edited: Nov 4, 2006
6. Nov 4, 2006

### lightarrow

Done. It was a disappointment, however, because I thought to find something more than what I studied at university 20 years ago; instead, it's still the same.
In about 80 years, physicists has never been able to make a better model of the electron than to think of a little ball? My compliments for the fantasy!

7. Nov 4, 2006

### ZapperZ

Staff Emeritus
Can you show me where physicists think an electron is a little ball?

Zz.

8. Nov 5, 2006

### Locrian

My condolences for the misunderstanding.

9. Nov 5, 2006

### lightarrow

Here:
I thought it was obvious I was answering to the this post; I will make it more clear, then: In about 80 years, physicist have never been able to find a better classical model for the electron than that related to the classical radius? I can't believe it.

I wonder why, talking about an atom behaviour, it's always said that this is one example of Classical Physics failure, since the only electron's classical model used to show this is the point-like electron. I mean, knowing now that an electron cannot be point-like, at least because it also has wave-like properties and because of the problems with infinite electrostatic energies and so on, it doesn't seem so strange to me that such a model of the atom couldn't work!

Locrian, is this clear or do you need me to explain it better?

10. Nov 5, 2006

### dicerandom

In Physics, "Classical" usually means "wrong" Nobody is saying that we should be modeling the electron as a rotating sphere. Every professor in every quantum mechanics course I've ever taken has made sure to explicitly state that is not the case, as a matter of fact. What they're saying is that if you want a simple model of an electron then a rotating sphere with this particular radius will get you a few of the right answers for the wrong reasons.

The classical model of the atom doesn't fail because the electron is approximated as a point particle, it fails because the radial states are not quantized. In the classical model of an atom you have an electron which orbits the nucleus in much the same way that planets orbit the sun. The problem here is that the electron is charged and accelerating due to the circular motion, so it should radiate. If it radiates it loses energy so it should lose speed and spiral in towards the center. If you work it out this whole process ends up taking about a nanosecond, so with that model we really shouldn't have any atoms at all.

11. Nov 5, 2006

### ZapperZ

Staff Emeritus
1. What does what you find googling for this is what "physicists" know? If you find crap about it from google, this somehow reflects what physicists generally accept? This is absurd!

2. What EXACTLY did you understand by the term "electron classical radius"? Hint: it is connected to an ATOM. This doesn't even come close to being the electron's SIZE! So why are you hung up on this?

This is precisely my point here that when you and others talk about the "size" of an electron or the "size" of a photon, you guys really are clueless on what you are refering to. Why else then are you now confused with the electron classical radius, or the de Broglie wavelength, both of which have NOTHING to do with the "size" of an electron. Whenever I see such utter confusion happening, it is either the issue is poorly understood, or someone is trying to use something in which a clear definition doesn't exist.

It seems that no one has actually learned anything from Special Relativity, or gained any lessons from it. The fact that we had to clearly and unambiguously define what we mean by "length" implies that when we explore the world beyond our standard classical limits, a lot of the normal quantities that we take for granted have to be re-examined carefully. Einstein realized that we take for granted that what we see come to use simultaneously. It is why we can measure the length of a rod without thinking of the amount of time that passes between light hitting both ends of the rods and back to our eyes. Yet, such assumption breaks down when that time instant no longer works. That is why we have to clearly describe how we measure such a length via a series of light pulses that we measure when each end of the rod passes through a particular location. This is where our concept of length gets turned upside down. But the point here is that we must clearly now define what we mean as a "length".

No such thing has been done for a "photon" or an "electron". Physics has no definition for such a thing. Don't believe me? Please hunt for a paper to prove this wrong. Your question is asking for an answer to a property that has not been defined. Now unless your intention is to do your own exploration, then you have to (i) make your own definition so as to be able to have someone answer it based on what you have come with with and (ii) do this in the IR forum, because this is now a piece of personal speculative discussion that isn't part of standard physics.

Zz.

12. Nov 5, 2006

### lightarrow

Yes, ok. What about a model in which the electron is, e.g., a wave packet spread around the nucleus, and that reabsorbs the same radiation it emits?

13. Nov 5, 2006

### lightarrow

14. Nov 5, 2006

### ZapperZ

Staff Emeritus
And my question was, why are you so hung up on this? And why are you accusing that this is all the physicists know all this while?

Are you going to accept this as THE definition of the electron size? If you are, then you shouldn't have bothered with the de Broglie wavelength in the first place, because they both contradict each other - y'know, one of the unspoken principle of physics, that when 2 things contradict each other, something has to give. You might as well throw out QM and especially the Standard Model while you're at it with this definition.

Hey, at the very least, you now have a "definition" for the size of an electron, no? Regardless of its validity, we can now lay this question to rest.

Zz.

15. Nov 5, 2006

### kvantti

16. Nov 6, 2006

### lightarrow

I'm not hung up on this at all, I intended to answer to tehno in an ironical way, sorry, it was not a good idea. I know very well how concepts of "classical electron radius" are nothing more than simbols. Indeed it's for these reasons I started this post. Anyway, if you wish, you can terminate it here. However, reading to every post helped me understand that it's impossible, for today physics to define a size for the electron.

17. Nov 6, 2006

### tehno

:rofl:
Why the irony?
I tried to answer your question in the best possible way I could.
"Classical electron radius" is somehow associated with electron but current state of physics don't know yet exactly how.Probably will never know exactly how.Your statement that physicists think of electron as charged little ball is a nonsensence.Why not to think like some string theorists and decide that the best "shape" representing it would be a donut?
These and other reasons is why in deriving ommited is factor 3/5.
This range of lenghts, in order of $$10^{-15}m$$, is characteristically met in accelerators when elementar charged particles collide and occurs as the threshold of "reactions".
You didn't do your homework right:Althought it is called "classical" ,this number is far from being just classical.It's closely related with other constants in quantuum physics and relativistic quantuum physics.

Last edited: Nov 6, 2006
18. Nov 7, 2006

### lightarrow

Ok tehno. So, which is your idea of the electron? Which is the model, classical or not, that best represent it, inside an atom and as a free particle? In your vision, is the electron's wavelenght (the average wav. of the wave packet) in some way related to the electron's "size"?

Last edited: Nov 7, 2006
19. Nov 7, 2006

### tehno

1.)I don't have any special idea of the electron except that it is fundamental particle ,a source of Coloumb field,without subdivsion property.
2.)Classical model definitely not. For the other part of the question I don't have idea which is the "best model" of the electron outside Standard Model(that one doesn't model bloody damn particle)
3.)I don't have a vision of the model of electron ,I have never seen a one in person.Electron wavelenght ,is not related to the electron size ,but it is related to circumstances of electron mass and velocity in the framework of known relations of quauntuum physics.

20. Nov 7, 2006

### lightarrow

Ok. Very well. So, having taken note of this, what does your answer:
has to do with my question:
?
It's much more easy to criticize than to say something constructive, did you know? If I want, I can be very good in just criticizing, believe me. Next time, why don't we try to discuss together of constructive things, instead of play the game of finding the other's failure? The same is true for ZapperZ.
Thank you.

Last edited: Nov 7, 2006