Is Dirac's equation valid for point charges?

[marlon]

The banter is indeed educational, but I'd like to ask my 3 questions again:

1. Is the electron a cloud in an atom and a point charge when it is free?

The electron (i mean, its structure) itself is always a point particle. The position however is not exact due to the HUP.

marlon

 

[masudr]

what_are_electrons last two questions are answered well by dextercioby. His first answer is good but brief. Let me elaborate.

You are asking if an electron is a point like particle or a cloud. The first thing to realize is that on the sub-atomic level you cannot imagine to electron as a tiny little ball, or even a dot. The reason is because such an image does not tell you much about the electron.

That is why to truly understand quantum mechanics you have to do a bit of the leg-work and get to grips with the mathematical formalism. Then the uncertainty principle will become clear, and all the answers to your questions will become clear (as clear as they can be with respect to QM). Until then, the best we can do is provide an answer that won't help your understanding.

As dextercioby says, an electron is always treated as a particle that has no spatial extension (i.e. is of size that tends towards 0). You may think that you have read in much popular scientific literature that there are electron "clouds" in atoms etc. That is a statement of our knowledge of the position of an electron. If we proceed to make a measurement of the position, we will find the electron in a definite place. But generally, we're not too bothered about exactly where the electron is, and all we do is provide a probability distribution of where the electron might be located. The best way to visualise this probability distribution is in terms of an electron cloud.

Bear in mind that the electron (according to all currently widely accepted theories, as dextercioby says) will always be found at a single point in space when it's position is measured. Hence an electron is a point-like particle.

 

[jtbell]

1. Is the electron a cloud in an atom and a point charge when it is free?

In our current understanding (which is of course always subject to revision based on new experimental evidence), the electron is always a point particle, whose position can be specified only by way of a probability distribution (your "cloud"). For an electron bound to an atom, the probability distribution corresponds to the "orbitals" that you can find pictures of in many physics and chemistry textboks. For a free electron, the probability distribution is a wave packet that has some width which causes an uncertainty in position at any particular time.

2. If the electron is indeed a cloud when it is inside an atom, then what is the mechanism for the electron to be freed from the atom and to form a free point charge?

Whether inside or outside an atom, an electron's position is always described by a probability "cloud."

3. Is it possible that experimental physicists will one day have the tools to measure the non-point size of the electron?

We already have measured the non-point nature of the electron's probability "cloud" in many situations. All these analyses so far, assume that the electron actually interacts as a point particle (with random position). If the electron did not interact as a point particle, we would have to add "form factors" to the analysis, which are related to the shape and size of the electron. So far this has not been necessary. It may become necessary in the future, depending on experimental data which is yet to be collected.

For a parallel situation, consider Rutherford's nuclear model of the atom. His analysis of his famous experiments on scattering of alpha particles by gold nuclei assumed that the nuclei could be treated as point particles, and his predicted angular distribution for the scattered alpha particles agreed with his experimental data. Later data using higher-energy alpha particles disagreed with Rutherford's prediction, and this was taken as evidence that atomic nuclei do in fact have a finite size.

Similarly, when we scatter electrons or neutrinos off of protons or neutrons, at high enough energies the angular distributions of the scattered particles disagree with what we would expect if protons and neutrons were point particles. This was first observed in the late 1960s, and led Feynman to produce his "parton model" in which protons and neutrons were actually collections of "smaller" particles. Further experiments showed that these "partons" in fact had the properties of the "quarks" that had been proposed earlier by Gell-Mann in order to explain the patterns of properties of particles in the burgeoning "particle zoo."

Something similar may very well happen with electrons in the future... but there's been no sign of it yet in experimental data on electron-electron, electron-neutrino and electron-positron scattering, as far as I know.

 

[sifeddin]

I still do not the (p)oint (p)article quite a clear cut of some (p)roof, (p)aradigm or even (p)ostulate of some (p)rofessor . If you do not get it read e.g. Ch. 7 of White "Basic Quantum Mechanics", for the Gaussian packet of psi function that represent the free elctron.

However, try to focus on the answer of this question which I wish "again" that Kane O'Donnell (whom i cought saying the words) may answer it in the most explicit way:
Is it Max Born who stated that the electron is the point particle with the psi (like the White's Gaussian packet one) is the amplitude of its probability density?

Well, I concentrate on the electron here because I read in some paper that A.E. once said if you really understand what the electron is you may understand all the physics. I do not quote here but I recall from memory but I imagine also that the proton was not discovered yet when he said that .

 

[dextercioby]

I'm not sure on whether he used the exact words "point particle" (i haven't read his article),but he definitely gave the Schroedinger wave functions the interpretation we have today.

As for A.E.opinion,would you care to recall when (in what year) did he assert that...?It may be relevant to a further discussion.

Daniel.

 

[sifeddin]

I'm not sure on whether he used the exact words "point particle" (i haven't read his article),but he definitely gave the Schroedinger wave functions the interpretation we have today.

Well I guess I am "certain" about that too. Kane! Help! please!

As for A.E.opinion,would you care to recall when (in what year) did he assert that...?It may be relevant to a further discussion.

Daniel.

Well my comment was a mere joke but I read it in paper on the new representation and geometric meaning of the Dirac spinor wave function when I find it (while reading the forum) I may post the reference for you.

 

[Kane O'Donnell]

Look, you can use a Gaussian wave packet as a way of representing a *localised* particle. This doesn't mean the particle we're representing isn't a point particle. The problem is that if you use say a delta function to represent a point particle, then the particle has a totally uncertain momentum and it's not very useful for modelling. On the other hand, if we're willing to accept a reasonably small uncertainty in position (by using a finite-width wavepacket) then we can get a reasonably small uncertainty in momentum.

Whenever anyone goes looking for the location of a single electron, they find it in a single place, and no scattering experiment has shown that an electron has a finite spatial extent.

Just remember that wavefunctions *don't* represent the *physical* size of a particle, they represent the probability of finding a particle (all of it) in a particular place.

Kane