# What exactly is spin?

1. Dec 6, 2009

### Char. Limit

I don't understand electron spin. What is it? Does spin have units? Does it do anything like electric charge or gravitation does? What does it represent? Any help for a "wikipedia physicist" (as I call myself) would really help. Just keep in mind: I haven't taken a class in QM.

2. Dec 6, 2009

### dextercioby

It's one of the fundamental attributes of a quantum system. It's in the same category with mass/energy. From a rigorous viewpoint, it's linked to the global rigid symmetry of a flat space-time. To put spin in general relativity requires some advanced tricks in differential geometry.

Last edited: Dec 6, 2009
3. Dec 6, 2009

### Char. Limit

Yes, of course, but, for example, what does spin measure, and in what units? Mass has kg, and energy has J...

4. Dec 6, 2009

### Fredrik

Staff Emeritus
If you haven't studied QM, you won't understand this, but you should look at it anyway, because it might give you an idea why no one is going to be able to explain it to you in a way you'll be entirely satisfied with. The extremely short version is that it's a property that we can see that particles must have if we combine the principles of QM with the assumption that space is rotationally invariant.

The result of a measurement of a spin component operator is expressed in the same units as angular momentum. In terms of units of mass, length and time, it's kg m2/s, but you could also express it as Js (Joule-seconds).

5. Dec 6, 2009

### dextercioby

Spin is the angular momentum (therefore it has units) of a quantum object calculated/measured in a reference system in which that object has 0 orbital angular momentum. One such system of reference is, of course, the one attached to the object itself.

Last edited: Dec 6, 2009
6. Dec 6, 2009

### Matterwave

You can think of spin as the intrinsic angular momentum of a particle (rather than say, orbital angular momentum).

E.g. If the Earth is moving around the sun, and rotating, the orbit is the regular angular momentum, while the rotation is the "spin" angular momentum.

This is JUST a tool to help you make the concept a bit more concrete. DON'T take it literally. Particles, as far as we know are point particles and therefore can't really spin like the Earth does. Also, if you take an upper limit for the size of the electron, and try to find out how fast it must "spin" then a "point" at the electron's equator would need to be moving faster than the speed of light. This is no good! So don't think of this analogy in the literal sense.

7. Dec 6, 2009

### Char. Limit

Thanks for all of these. My first mistake, I think, is that I thought of spin as literal, and couldn't figure out how electron clouds could "spin". Now I see the truth: I will not understand without much more background knowledge than wikipedia can provide. (it might help to know more about eigenstates than I can figure out from German, for example)

Thanks!

8. Dec 6, 2009

### ytuab

It is very difficult for you to consider electron spin as real spinning.

The main reasons are as follows,
1 The electron size is too small, so by equating the angular momentum of the spinning sphere of the electron to 1/2hbar, the electron sphere speed leads to more than 100 times the speed of light.

2 The spinning electron will not go back to their original forms when they are rotated by an angle of 2 pi.
(This is called "two-valued", so when the angle is 4 pi, they go back.)

To speak simply, Spin is "a magnetic moment", because the magnetic moment can be measured by the real experiment.

But why we call it "spin"? To know that reason, we have to understand the spin history.
The most important phenominon of this was "an anomalous Zeeman effect", I think.

Because it is possible that the Stern-Gerlach experiment and the fine structure (energy difference between 2P1/2 and 2P3/2) can be explained also by the Bohr-Sommerfeld model. (For example, see this.)

They tried to explain about the many spectrum lines under the magnetic field using the spin-orbital interaction.
(But to be precise, the one electron atom hydrogen usually shows the normal Zeeman effect. and Lithium tend to show Paschen-Back effect. So the anomalous Zeeman effect is a little complicated to explain.)

Sorry for a little long story.

9. Dec 6, 2009

### Neo_Anderson

As others have said, spin is intrinsic angular momentum, and is assigned discreet values (unlike continuous values for orbits or rotation). The electron, eg, has two discreet (key word) values: 1/2 and -1/2 spin.

Please understand that the guy who coined the intrinsic angular momentum of a particle as "spin" is a complete imbicile. The term is misleading.

For the electron, "spin" is synonymous with "charge." You have a positive charge (same as +1/2 spin) and a negative charge (same as -1/2 spin).

10. Dec 6, 2009

### Neo_Anderson

11. Dec 6, 2009

### Char. Limit

Wait, electrons with positive 1/2 charge?

12. Dec 6, 2009

### dextercioby

It's just a convention that they have -1/2. They could have very well had +1/2 and their antiparticles -1/2.

There are, probably, 10 or more places in physics where "sign" conventions occur. Surely, one is forced to reconcile them all to get a clear picture.

13. Dec 6, 2009

### Char. Limit

Don't electrons have both positive (up) and negative (down) spins? I seem to remember that from AP Chem...

14. Dec 6, 2009

### Matterwave

up and down spins are just the 2 "degrees of freedom" afforded to the electron. The electron's spin can either be directed in the direction of the positive Z axis or the negative Z axis - giving you both up and down. This is completely dependent on how you define your Z-axis.

15. Dec 6, 2009

### dextercioby

The "up" versus "down" issue is probably linked to a convention to disseminate the 2 independent eigenvectors for the spin operator of a spin 1/2 system:

$$\left|\uparrow\right\rangle =\left|\frac{1}{2},\frac{1}{2}\right\rangle$$ and, of course,

$$\left|\downarrow\right\rangle =\left|\frac{1}{2}, -\frac{1}{2}\right\rangle$$

16. Dec 6, 2009

### Char. Limit

OK, I think I might be getting a (very) basic idea now. One thing confuses me though: how can electron "spin" be synonymous with charge, if an electron has one possible value for charge, and two for "spin"?

Also, in the equation for the post above, what are those strange | and > symbols?

17. Dec 6, 2009

### Matterwave

Spin is not synonymous with charge. It is, however, linked to the magnetic moment.

That's bra-ket notation he's using. Those | > symbols represent a "ket". It's a vector in Hilbert space.

18. Dec 6, 2009

### Char. Limit

OK... I looked up the magnetic moment, and found that the unit for that is J/T. Soo...

If magnetic moment and angular momentum are related by a g-factor of 2 (why 2?), does this g-factor have a value of 2 T/s?

Or am I just insane?

(Also, what is a "magnetic moment" in macroscopic, or at least understandable terms?)

Progress is being made, I'm closer to understanding than I was before. Don't give up on me now! (Not that you would)

19. Dec 6, 2009

### apeiron

If you want another way of looking at it, you are doing the natural thing of thinking of the electron as a spinning ball. But instead, how about thinking of a point particle as a location that arises by the kinds of questions we ask.

So to start with, anything might be "there". Then we narrow down the there-ness to what might exist at a point.

It is a little like coralling sheep into a pen perhaps. First they are possibly all over the place, and then we constrain their location.

Then having located there-ness to a 3D point, there are still aspects of this point that remain as yet unconstrained. Like a potential to be rotating on the spot. Further questions can then polarise this point - fix a direction and quantity of spin.

So just see spin as the last refuge of freedom for something that has already been restricted to a spatial point. Then we can go in and constrain that aspect of its freedom as well.

With the sheep in a pen analogy, you can see we may have confined them to a point, yet we have not yet stopped them milling about. And maybe we can imagine polarising the state of those sheep by some kind of measurement, like having the sheep dog go in or do something else that makes them line up in some coherent circular fashion.

The sheep could potentially be going in many directions (well not many as the pen is a 2D plane rather than 3D sphere) and then measurement limits the action - it imposes a further constraint on the system's naked freedoms.

20. Dec 6, 2009

### Char. Limit

...
...
That sheep-in-a-pen analogy may be (no offense to the others) the best I've seen yet. Just one thing. An electron is an area of high probability, not a particle, so it's... not a 3-D point? Or am I assuming something stupid again?