# How do electrons move?

1. Nov 24, 2007

### Brock

Do they spin, or orbit around the nucelous of the atom?

2. Nov 24, 2007

### christianjb

Very crudely- an electron is smeared out like a cloud around the +ve nucleus.

It is possible to make measurements of the rotational angular momentum of the electron and get 'sensible' answers, but quantum mechanics is weird. Strictly speaking, the electron can't be viewed as having an instantaneous position and velocity like macroscopic objects. Its properties are more 'blurry'.

This applet might give you some idea

3. Nov 28, 2007

### Brock

thanks. Is that 2 hydrogen atoms bonded together that I'm looking at?

4. Nov 28, 2007

### cesiumfrog

ooh, 3D rotating orbital density plots, that's quite nice. And it's just the one atom, Brock.

5. Nov 28, 2007

### vincentm

Is that mostly due to the uncertainty in knowing it's position and momentum simultaneously?

Oh ok, i see what you're getting at.

That's pretty neat, my understanding is a bit more clear now thank you. I've seen this picture of the electron before in a book, but wasn't sure how it actually depicted it.

6. Nov 28, 2007

### christianjb

7. Nov 28, 2007

### Brock

what's the 2 more circular, and dense spots then? where's the nucleous? The centre is empty, certianly the nucleous is in the centre of the atom??

8. Nov 28, 2007

### cesiumfrog

Brock, the nucleus would be too small to see on that scale.. you're only looking at the electron cloud (in different possible states.)

9. Nov 28, 2007

### christianjb

The dense regions of the cloud are regions of higher probability.

The Applet when loaded up shows a particular 'orbital' of the electron. There are many different possible orbitals the electron can be in and each corresponds to a stationary state in which the probability doesn't change with time. It also corresponds to a state of definite energy.

The electron (or its wavefunction) can also be in a combination (mixture) of different orbitals- a bit like the difference between one note and a chord. In the case of a mixture of different orbitals the orbitals 'beat' against eachother like two close notes on a guitar to produce motion of the probability distribution as a function of time.

Anyway- the orbital shown is not the most likely one for the electron to be in. The electron is more likely to be in the 'ground-state' orbital- which is the orbital of lowest energy. A picture of that orbital shows a nice spherical cloud distribution about the nucleus.

10. Dec 2, 2007

### LeoYard

Can anyone explain why does an electron have intrinsic spin? Pauli and Dirac matrices show the existence of spin, but this doesn't really explain the physical origins of the spin.

11. Dec 2, 2007

### belliott4488

Excellent question, and one that leads to very profound consequences. There are numerous explanations for this to be found (Google is your friend), but let me take a stab and see how this strikes you.

Much of Quantum Physics -- and physics in general, really -- is concerned with conserved quantities, and the intrinsic spin of electrons (and all fermions, for that matter) is one of them. There's an important theorem, called Noether's Theorem, that relates symmetries of nature to conserved quantities; in short, for every symmetry there is a conserved quantity.

The reason that we have particles with intrinsic spin actually has to do with the symmetries of space-time. You don't get spin automatically unless you're working with relativistic mechanics, with its space-time symmetries. Without getting too deep into it, I'll just say that it turns out that the space we live in has the property that not everything is unchanged by a rotation of 360 degrees - some things pick up negative signs. Those things require a rotation by 720 degrees in order to return to their initial state. Electrons have this kind of symmetry, and that's what leads to their intrinsic spin.

That probably isn't very satisfying, if you're thinking of electrons like little spinning tops, and you'd like to know what got them spinning. You won't ever be satisfied, however, if you think of them that way. Spin is definitely a kind of angular momentum, but it is not due to rotation of an extended object - it's really a fundamental quality of the particle, which just happens to have the characteristics of angular momentum. Ultimately, that fundamental quality comes from the symmetries of that particle under rotations in space-time.

Make sense??

12. Dec 2, 2007

I think that it is fair to say that the internal spin of an electron will always be confusing in the QT scheme of things. QT simply has no ontology to explain the nature of such things, no quantum model with which to picture these things. They will always remain obscure.

It is important to distinguish between intrinsic spin and orbital motion. In the old quantum scheme of things, the electron was suppose to have a quantum orbit around a proton, or nucleon if you prefer. The problem being that its angular momentum was supposed to be divided over the entire orbit into quantum amounts. So if you have an angular momentum mvr, you are really concerned with:

$$mv(2 {\pi} r)=nh$$ Bohr's quantum restriction postulate.

So it could be said that h is $$mv(2\pi r)$$ and it occurs in quantum amounts over an orbit. The question then became: what defines or creates the multiples of h. Some suggest that n is the intrinsic spin of the electron. The problem is that this approach deals with the electron as a particle with a trajectory. The problem being that it only worked for Hydrogen, and even then it led to major difficulties. The way we treat electrons now, is statistical, and its position and time take on a distribution. So the electron is no longer treated as a particle, rather its location is spread out to represent the likelihood of where and when it will be. So we see all of its positions in a density sense, in the applet. In the quantum scheme of things, the electron takes on this 'picture'. The problem I have is that once we make a measurement, that it is found in a definite position. So for instance, it may exist spread out and possibly in any number of paths, but it will always strike a detector in a single point.

If an electron has a spin, the question is whether this has an uncertainty applicable to it. Certainly, an electron can orbit a proton in one of two directions, clockwise or counterclockwise, and in that respect there is an uncertainty applied to it. The problem being that if the electron has an intrinsic spin applied to it that is always in one direction, does this mean that the positron has the opposite? If this is the case, then whenever you measure the internal spin of an electron, the positron will always have the opposite.

In the quantum scheme of things this creates a paradox, because there is supposed to be an uncertainty attached to the internal spin. If for instance, you find that a positron and electron formed through the decay of a pion, always have opposite spin, well there is the paradox.

This leads to the question of nonlocality versus locality. Does the measurement of one spin affect the other. Does the electron act over a distance to influence the spin of the positron. Some argue that the spins are predetermined, at the origin of their creation, when the pion decays, and in that respect they will always be opposites...

I've gotten into a lot of philosophical problems when arguing that a intrinsic spin implies that the electron has size. You see, the electron is treated in QT as a point particle, mathematically. Second, there is no evidence that it has any internal structure, unlike the proton which has internal structure. The simple argument being, that if an electron has internal spin, what does this mean in a physical sense? What spins? For it to have any logical internal spin, something must spin?

The inevitable problem is that QT does not have a model in a classical sense, so it takes on a twisted philosophy of its own. In the absence of such a model, the way it treats the electron mathematically, becomes the philosophy, the ontology, the picture we are forced to accept. It remains that QT creates paradox's and that we must accept that the nature of that microscopic quantum realm is as it is. In a classical scheme it is just as inexplicable, so QT wins the argument.

Epistemologically speaking QT deals with the knowledge 'that exists' and not the knowledge 'how that exists'. So when you ask a question, How does the electron have... this or that? You will always get someone stabbing at the solution. It is an obscure science, and we tolerate that obscurity, because it leads to successful results.

Last edited: Dec 2, 2007
13. Dec 2, 2007

### cesiumfrog

Could you perhaps give a citation to where this 720-as-specifically-opposed-to-360 thing is shown to give rise to spin? I find it quite.. surprising, since as far as I knew there was no way to actually observe this lesser-symmetry of the spinor/wavefunction.

There's an argument that intrinsic spin is actually due simply to a rotating current of the electron's wavefunction (just like orbital spin, for that matter). I've probably cited the article on PF before (it's also in the footnotes of Griffiths).

14. Dec 2, 2007

### belliott4488

Oh, gosh ... I was just thinking of the explanation that is often given when Dirac spinors are first introduced for describing the possible states of an electron in relativistic QM. Not having any quick references on the top of my head, I just did a Google search for "Dirac scissors", as this problem is often called, after the famous demonstration by Paul Dirac. He used a pair of scissors with a string looped the handles and tied to the back of a chair. Rotate the scissors once and the string is irretrievably tangled, but rotate through another 360 degrees, and the string can be untangled without further rotation of the scissors. In other words, the final state (after 720 degree rotation) is equivalent to the initial state in a way that the intermediate state (after 360 degrees) was not.

Here are some of the results that popped out of Google:
from sci.physics.research: http://www.umsl.edu/~fraundorfp/p231/spinexcl.html
from Wiley (the Google reference looked more helpful, but frankly this abstract looks fairly advanced. I included it for those who are interested): http://www3.interscience.wiley.com/cgi-bin/abstract/112425063/ABSTRACT?CRETRY=1&SRETRY=0

If you are familiar with the groups O(3) (rotations in the space of 3 real dimensions) and SU(2) (rotations in the space of 2 complex dimensions), they are very much related to this. Some factoids:
- You can say that two "copies" of O(3) fit into SU(2), which is the "covering group" for O(3).
- O(3) can be represented by ordinary 3x3 rotation matrices; SU(2) can be represented by 2x2 unitary matrices, which in turn can be spanned by the 2x2 identity matrix and the Pauli spin matrices, which also form a basis for the quaternions, which are also a way of representing 3-d rotations, albeit with a factor of 1/2 in the angles (!!!).

This stuff is pretty mystifying, and I readily admit that I don't really get it all, but there's something fascinating about it all ....

15. Dec 2, 2007

### belliott4488

16. Dec 2, 2007

### cesiumfrog

That second link was cute, linking the practical platelet centrifuge to a candle dance and spinors.
I was more wondering why you said this particular symmetry gives rise (through Noether's theorem) to intrinsic spin? For example, does the same reasoning imply Dirac's scissors also have a separate intrinsic angular momentum?

17. Dec 3, 2007

### LeoYard

I'm also wondering about what you wrote: "... this particular symmetry gives rise (through Noether's theorem) to intrinsic spin...". Sure. But what does it mean? From a strict physics point of view, how can an intrinsic property act in the same way as a motion, without being motion itself? Very bizarre.

18. Dec 3, 2007

### belliott4488

Well, I can confirm the "very bizarre" part - about the rest, I'll just have to wing it and hope I'm not too far off the mark.

First, I'm not sure that spin acts "in the same way as a motion." True, it is measurable and has units of angular momentum, and it does give rise to things like magnetic moments ... but I don't think there is anything that actually behaves like a rotating object. In other words, you can't say that the electron is "spinning at rate omega" and then expect that after a time delta-t you can observe that it has rotated through an angle omega*delta-t. (By "rotation" I would mean that the "before" and "after" states could be related by a rotational transformation through that angle.) It just doesn't work that way, because electrons don't have "sides" or any other features that would allow you to say that they'd rotated through any angle.

Unfortunately, while I am reasonably confident about saying what it's not, I really have little idea how to say what spin is. It is a conserved intrinsic property, like charge or color, and is also related to a symmetry of nature. That has something to do with how objects behave under rotations, but since we're not talking about small solid objects, that's difficult to picture.

As for cesium frog's question about Dirac's scissors ... no, of course we wouldn't want to say that scissors have spin 1/2. I think that demonstration was meant to show one example of a symmetry that is not invariant under a rotation of 2*pi but is invariant under a rotation of 4*pi. There might be a deeper mathematical connection (through topology, maybe?), but I don't know what it is. I've never been clear on how the scissors explain electrons' properties, to tell you the truth.

Sorry not to have a better answer than that ...