The Spin-Up/Spin-Down Effect in the Stern-Gerlach Experiment

[touqra]

A book that I've read says that there is no Stern-Gerlach experiment for electrons or protons because they carry electric charges and the Lorentz force will deflect them differently. But even if the Lorentz force deflect all of them upwards or downwards, won't they still separate slightly into two groups, due to spin up and spin down ?

 

[Mr.Brown]

yes i think they would but designing an appropriate experiment would get rather tricky because charged particles would easily get trapped in the field on some circular orbits in case of the needed magnetic fields even so they are inhomogeneuous.
On the other side predictions would also get pretty involved if you have to take account for the charge of the particle.

 

[Meir Achuz]

SG requires an inhomogeneous B field. This produces a spread in angle of a charged beam that is as large as the difference in angle of spin up and spin down.

 

[touqra]

SG requires an inhomogeneous B field. This produces a spread in angle of a charged beam that is as large as the difference in angle of spin up and spin down.

I never thought of the inhomogeneous B field by the magnet system, one shaped like a triangle, the other magnet placed opposite to it, a rectangle. I thought it was some experimental limitations. In principle, you can do the spin up-spin down splitting just by having a homogeneous B field that points straight in the z-direction, no ? Something like a needle like magnet...

 

[RandallB]

A book that I've read says that there is no Stern-Gerlach experiment for electrons or protons because they carry electric charges and the Lorentz force will deflect them differently. But even if the Lorentz force deflect all of them upwards or downwards, won't they still separate slightly into two groups, due to spin up and spin down ?

What book is that??
Were they actually asking people that had really done Stern-Gerlach experiment with electrons?
Or just jumping to their own conclusions that no one has ever done one with electrons.

Stern-Gerlach experiments are not easy
And of course if you send a point charge particle through a dense horizontal magnetic field the charge will always be diverted in one direction – for our example use “up”. Think the problem through – what do you want to do about the problem. You don’t have a Stern-Gerlach experiment you have a magnetic experiment – how do you want to fix it to keep electrons going straight? More than one way to divert a point charge - CRT’s use electrostatic fields too.

So one way is to add charged plates above and below so that while the magnetic field pushs the “point charge” UP. You design an electric field that pushes it down. Net result is a point charge particle that goes though our device in a perfectly straight line.
Now that is longer a simple magnetic experiment like “that book” assumed. We can send charged particle though a magnetic field in a nice straight line. And we should expect them to stay in a straight line unless they are not true point charges. The fact that they don’t stay straight and go to one of two places on up and one down tells us two things. One; There must be some kind of “spin” going on. Second, since it diverts the same amount, not a little up and a lot up fro an average amount of up. The value of spin comes in fixed whole units. So we find particles come with multiples of ½ Spin amount of spin (including zero).

Stern-Gerlach experiments may be tricky to understand but they are not all that tricky.
If you want something hard to explain try explaining spin without FTL rotations.

 

[Meir Achuz]

I never thought of the inhomogeneous B field by the magnet system, one shaped like a triangle, the other magnet placed opposite to it, a rectangle. I thought it was some experimental limitations. In principle, you can do the spin up-spin down splitting just by having a homogeneous B field that points straight in the z-direction, no ? Something like a needle like magnet...

There is no force on a magnetic moment in a uniform B field. That is why the funny shapes are used to produce an inhomogeneous field.
Read about magnetic moments in an intermediate or graduate EM book.

 

[damgo]

In principle, you can do the spin up-spin down splitting just by having a homogeneous B field that points straight in the z-direction, no ? Something like a needle like magnet...

Nope. It's true that spin-up and spin-down particles have different energies in a homogenous B field. (They will differ by $$\Delta E = 2 \mu B$$.) But since this is a constant difference, there will be no force -- remember $$F=-\nabla E$$.