What Dictates the Spin Direction of an Electron?

[Ryan Reed]

Spin is an intrinsic property of particles meaning that they have it naturally. Electrons can have either +1/2 spin or -1/2, what dictates that it is one instead of the other?

 

[fzero]

Spin is an intrinsic property of particles meaning that they have it naturally. Electrons can have either +1/2 spin or -1/2, what dictates that it is one instead of the other?

We do when we choose the convention for + vs -. Nature doesn't care which is which, it only knows that they are different.

 

[Ryan Reed]

Then what is the difference? How could one tell that the electron has a +1/2 or a -1/2?

 

[fzero]

Then what is the difference? How could one tell that the electron has a +1/2 or a -1/2?

Google for Stern-Gerlach experiment. Briefly, in an external magnetic field a magnetic dipole has an interaction energy $H_d = - \vec{\mu}\cdot \vec{B}$. Spin up and down have opposite signs in this formula (if all else is equal), so you could conspire to make a measurement that would distinguish them.

 

[Ryan Reed]

And is the spin of the particle static, as in it doesn't change? Or can particle spin be flipped and changed?

 

[fzero]

And is the spin of the particle static, as in it doesn't change? Or can particle spin be flipped and changed?

If we have a particle that we know to be in a definite spin state, then the spin can be flipped if we interact with it. From the same interaction, we can imagine that we can apply a nonconstant field that will rotate the dipole. If the dipole has rotated enough to now have the negative projection onto what we have decided is the axis we are using to measure spin, then we would say that the spin has flipped. This is really a classical point of view though. In the quantum picture, we are adding a small bit of the spin down state to the quantum state when we turn on the field. So there is always a nonzero probability to find that the spin has flipped due to the applied field. Tuning the field can have the effect of increasing the probability that the spin flips.

 

[Ryan Reed]

How would you find these dipoles? I'm guessing that there is some way to tell since the magnetic field isn't distributed in the same way on the equator as on the poles.

 

[fzero]

How would you find these dipoles? I'm guessing that there is some way to tell since the magnetic field isn't distributed in the same way on the equator as on the poles.

A particle with intrinsic spin is already a magnetic dipole, with dipole moment proportional to the spin vector. One learns this from the Stern-Gerlach type experiments that I've already mentioned.

 

[Ryan Reed]

Thanks! This is exactly the kind of answers I was searching for!

 

[Vanadium 50]

Electrons can have either +1/2 spin or -1/2, what dictates that it is one instead of the other?

Choice of coordinate system. Stand on your head, and everything flips sign, but the observable quantities remain unchanged.