Quantum Query

[Perfection]

Again, to be honest, at the level of an individual electron, I tend to see mathematical formulas whirling around, because I don't have a good analogy to visualize an electron.

I just imagine electrons as blobs of probability density.

 

[betazed]

Maybe a little insight into spin of particles is in order over here.

In QM spin has nothing to do with spinning/rotating but rather has to do with rotational symmetry. For, example take the + sign. In 2d how many degrees do we have to rotate it till it looks exactly like a + sign again? 90 degrees. So QM wise its spin in 360/90 = 4. Similarly, the minus sign has spin 2. Curiously, in 3d you can have topological objects that you have to turn 720 degrees (i.e. twice) for it to look the same again (imagine a twisted belt). These objects will have spin 1/2. The electron (and all spin half particles) are like a twisted belt.

So when we say an electron has spin 1/2 we do not mean that it is rotating like a ball and it has a wee bit angular momentum because of this rotation. But rather its geometry is such that it has to be rotated twice to look the same. Now you can see why its spin will always be there no matter whether it is at absolute 0 or whatever force you apply to it etc. You can never change the geometry of the electron whatever you do.

The direction of the spin (the spin-up/spin-down) thing is basically the two ways of observing the spin (whether you are seeing it as turned once or turned twice).

Now why just geometry turns out to be actual angular momentum in experiments (because you can actually measure electron's angular moment) is a bit tricky to explain. The easiest way to do it is that even in classical mechanics angular momentum - and the conservation of it - is really a result of rotational symmetry (isotropy of space) just like linear momentum - and the conservation of it - is a result of translational symmetry (homogeneity of space). Hence, this behavior just carries on unchanged into QM from classical mechanics.

The relation between spin/geometry and statistics is more difficult to explain. In fact I do not understand it well enough to explain it in simple words.

 

[Sidhe]

That's a very good description did you ever think of being a teacher? Now if you could explain the pairing of electrons at temperatures close to 0 degrees kelvin in a non visual form were all set

 

[Bozo Erectus]

That's a very good description did you ever think of being a teacher? Now if you could explain the pairing of electrons at temperatures close to 0 degrees kelvin in a non visual form were all set

Its like this, see, the electrons...oh damn, theres the doorbell! Gotta go, I'll let betazed explain it instead

 

[betazed]

That's a very good description did you ever think of being a teacher?

thank you.

Now if you could explain the pairing of electrons at temperatures close to 0 degrees kelvin in a non visual form were all set

You mean Cooper pairing? That's easy.

Take a ball that is painted red on one side and black on the other. Now how many degrees do you have to spin it to look the same. 360. So it has spin 1. Now take two balls each with red on one side and black on the other. Position them side by side so that one of them has red facing you and the other has black facing you. Now how many degrees do you have to rotate the entire system so that it looks the same. Still 360.

But there is a caveat. You can now rotate each ball just 180 degrees and switch their places. If the balls are indistinguishable (and electrons are indistinguishable) then it will look the same. So we can say that the individual objects of the system now has spin 2.

So you see how you can take spin 1 objects and combine them to make a spin 2 system. Exactly, the same kind of thing happens with electrons near absolute zero. Spin ½ electrons combine to make spin 1 systems.

 

[Perfection]

I haven't heard much about this sort of symmetry arguement for spin angular momentum. You wouldn't happen to know some good (and preferabely cheap) references on it?

 

[betazed]

I haven't heard much about this sort of symmetry arguement for spin angular momentum. You wouldn't happen to know some good (and preferabely cheap) references on it?

the run of the mill QM books do not teach with insight. But good books do. Hence, and unfortunately so, they are not cheap. I will recommend the following books to anyone trying to learn QM.

There is another cheap classic which deals with all of this but it requires a lot of math knowledge and you may not be ready for it yet. But definitely do read it in due course if you are interested in particle physics.

 

[Perfection]

Thanaks for the book info

But there is a caveat. You can now rotate each ball just 180 degrees and switch their places. If the balls are indistinguishable (and electrons are indistinguishable) then it will look the same. So we can say that the individual objects of the system now has spin 2.

Now here's a wild question...

What if it's not indistiguishable? What if we have an electron and a muon? What sort of possibilities does this lead to?

It seems to me that either such a pairing couldn't occur, or your analogy is incomplete.

 

[Sidhe]

Jehosophat there expensive Thanks for the link though.

Can I ask where you studied physics? You seem to have a very good grip in that your explanations leave little room for the imagination. This spin 1 system produces superconductivity yes, how exactly? I have to admit my knowledge is fairly basic in this area.

 

[7ronin]

I see why exactly? And please don't give me a link that is a text book, I don't have a huge volume of physics text books, I'd ask if you could provide a link on the internet if possible please?

I'm sorry I don't have any links or references to physics textbooks which might explain this. I think though that anything about Hans Bethe might discuss this topic since he was the first one to work out the principles of stellar nucleosynthesis.

Stars convert hydrogen into helium through nuclear fusion. They do this by raising the temperature (or kinetic energy if you will) of hydrogen protons to the point where the mutual coulomb force repulsion is overcome permitting the protons and neutrons to combine into helium atoms. To put it another way in the context of the OP, stars create helium by destroying the electromagetic fields of hydrogen atoms.

 

[Perfection]

Fusion don't destroy the EMF it just overcome it. It's the same way a magnet overcomes gravity when it picks up a nail. Gravity is still there, it's just being superceded by something else.

I nuclear fusion the EMF doesn't go away it just get moved around.