Can the Stern-Gerlach experiment accurately measure electron spin?

[cragar]

If we shot electrons down a magnetic field like in the SG test , the beam would split into
2 beams the spin up electrons and the spin down electrons would go one way . and if we took those individual beams after we separated them , and we did the same to those beams
if would also spilt into 2 beams because the first time we did it , the fact that we observed messed up the test . is this correct .

 

[Frame Dragger]

If by "messed up the test" you mean that decoherence had occurred as a result of measurement, then yes. If you're asking if you could take a,b beams, and split them into a', and b' beams for a total of a,b,a',b'... I think you would need a different apparatus. A BSM test with lasers could do that, but I don't think it would be possible in the SG setup.

 

[Matterwave]

I think in a SG experiment, if you used electrons, the electrons would all go the same direction due to the Lorentz force. I think you hafta use a neutral particle...

 

[Frame Dragger]

I think in a SG experiment, if you used electrons, the electrons would all go the same direction due to the Lorentz force. I think you hafta use a neutral particle...

Right, ok so silver or gold atoms, or even neutrons.

 

[Fredrik]

If by "messed up the test" you mean that decoherence had occurred as a result of measurement, then yes.

There will only be decoherence if the particles interact with something, like a particle detector. If the path is long enough or the density of the surrounding air is high enough, I suppose decoherence could also occur as a result of interactions with the air. But the Stern-Gerlach magnet alone isn't going to cause decoherence.

If you're asking if you could take a,b beams, and split them into a', and b' beams for a total of a,b,a',b'[...] I don't think it would be possible in the SG setup.

What's wrong with just using three magnets?

If we shot electrons down a magnetic field like in the SG test , the beam would split into
2 beams the spin up electrons and the spin down electrons would go one way . and if we took those individual beams after we separated them , and we did the same to those beams
if would also spilt into 2 beams

So far so good, except that you need to use neutral particles, as you have already been told.

because the first time we did it , the fact that we observed messed up the test . is this correct .

You haven't described an observation, so I don't understand what you're asking.

 

[xlines]

If we shot electrons down a magnetic field like in the SG test , the beam would split into
2 beams the spin up electrons and the spin down electrons would go one way . and if we took those individual beams after we separated them , and we did the same to those beams
if would also spilt into 2 beams because the first time we did it , the fact that we observed messed up the test . is this correct .

I am not sure what are you asking, but it may be this: you take up a beam of neutral particles with dipol moment and lead it through SG apparatus. Beams split up into two beams (S=1/2 let say). If you do that again for any resulting beam, they will not split again, as long as direction of gradient of field is unchanged. This is so because in one beam, all particles have spin up, so they go one way, and reverse for the other beam.

 

[cragar]

so the second beam won't split because they are all spin up or spin down , but what if we measured the particles right before they got split , could this possibly disturb them in such a way that the they could split a second time.

 

[xlines]

so the second beam won't split because they are all spin up or spin down , but what if we measured the particles right before they got split , could this possibly disturb them in such a way that the they could split a second time.

Time does not matter here. All it matters is how you direct your magnets. Let say beam goes forward and you orient your SG in the up-down direction. Then, it will split beams so one goes up, other deflects down. If you use up-down SG again on up or down beams any number of times, they will not split no more.

BUT if you orient your magnet left-right, and use it on up or down beam, they will split - one will go left, other will go right.

Here comes the twist: if you use up-down SG on a left or right beam, they again will split up or down =) That is so because left-right SG apparatus "disturbs them" so they "forget" their up or down direction.

 

[SpectraCat]

so the second beam won't split because they are all spin up or spin down , but what if we measured the particles right before they got split , could this possibly disturb them in such a way that the they could split a second time.

Not sure what you mean here again ... if you perform a second measurement on the "up" beam, the result depends on the relative orientations of the field gradients in the two magnets. If the first magnet was oriented along the z-axis in the lab, and the second magnet is oriented along the same axis, then there will be no splitting of the beam. However, if the second magnet is aligned along a different axis, then the beam will split ... the proportions of the split beam depends on the angle between the two magnets. If it is 90º (i.e. the second magnet is along the x-axis), then the beam will be split into two equal components, which will now be deflected left and right instead of up and down.

I hope this is clear, but there a a lot of important details about *why* this happens that would be silly to reproduce here. This is explained in lots of books, Sakurai's "modern quantum mechanics" has what I think is a particularly good account in the first chapter. The wiki page has some details, but is a little sparse. I haven't done an exhaustive search for good websites on the subject, but I'll bet they exist.

 

[cragar]

thanks for the answers , it is more clear now . As stated above i was told i need to do this test with a neutral particle , so would the photon work for this test it has spin .

 

[SpectraCat]

thanks for the answers , it is more clear now . As stated above i was told i need to do this test with a neutral particle , so would the photon work for this test it has spin .

That is an interesting question ... I don't actually know if one could work out a relativistic version of SG that would work for photons. I can see a whole host of issues that would need to be addressed carefully, but I think you might actually be able to generate a Doppler shift between the different helicities of photons (left-handed and right-handed), assuming that you had a SG magnet that was long enough to generate a sufficiently interaction to observe a shift. [STRIKE]I guess this has probably been worked out .. does anyone know a reference?[/STRIKE]

EDIT: The above paragraph may be irrelevant, as pointed out by xlines below. It should be prefaced by the comment, "if a magnetic gradient produces a non-zero interaction with a photon", and it is not at all clear that it does (I need to check this).

One important point is that it would not be possible to "split" the beam in the manner that we have been discussing, because the projection of the angular momentum of a photon is always either parallel or anti-parallel to it's direction of travel (i.e. linear momentum). In order to generate a transverse force necessary to observe a splitting, there has to be a projection on an axis transverse to the direction of travel.

 

[xlines]

That is an interesting question ... I don't actually know if one could work out a relativistic version of SG that would work for photons.
I can see a whole host of issues that would need to be addressed carefully, but I think you might actually be able to generate a Doppler shift between the different helicities of photons (left-handed and right-handed), assuming that you had a SG magnet that was long enough to generate a sufficiently interaction to observe a shift. I guess this has probably been worked out .. does anyone know a reference?

I am sorry, but now I don't understand. Gradient of magnetic field is interacting with particle's magnetic dipole moment, not it's spin a.k.a angular momentum. Run by me again, how does magnetic field interact with photon spin? Wouldn't that require nonzero gyroscopic constant?! AFAIK that is zero for photons.

 

[SpectraCat]

I am sorry, but now I don't understand. Gradient of magnetic field is interacting with particle's magnetic dipole moment, not it's spin a.k.a angular momentum. Run by me again, how does magnetic field interact with photon spin? Wouldn't that require nonzero gyroscopic constant?! AFAIK that is zero for photons.

Yes, I was too hasty in posting ... I was thinking about electrons simply as "spins", and of course it is the gyromagnetic ratio that is important for interaction with a magnetic field. Since that arises from the charge of the particle (at least in the simple treatment I am familiar with), it certainly seems reasonable to assume it would be zero for a photon. That said, I am not familiar enough with QED to know if this is strictly true when relativistic effects are taken into account .. after all, a photon *does* have a magnetic field.

Anyway, it is certainly not a simple as I implied from my initial casual analysis, thank you for catching my mistake.

 

[Frame Dragger]

So... the W and Z bosons have non-zero gyromagnetic ratios?

 

[xlines]

Yes, I was too hasty in posting ... I was thinking about electrons simply as "spins", and of course it is the gyromagnetic ratio that is important for interaction with a magnetic field. Since that arises from the charge of the particle (at least in the simple treatment I am familiar with), it certainly seems reasonable to assume it would be zero for a photon. That said, I am not familiar enough with QED to know if this is strictly true when relativistic effects are taken into account .. after all, a photon *does* have a magnetic field.

Anyway, it is certainly not a simple as I implied from my initial casual analysis, thank you for catching my mistake.

These things happen. Cheers!

 

[xlines]

So... the W and Z bosons have non-zero gyromagnetic ratios?

Huh?

 

[Frame Dragger]

Huh?

I was wondering if the W and Z bosons (weak nuclear force) are like photons, with 0 gyromagnetic ratios, or if their's is non-zero.

 

[xlines]

I was wondering if the W and Z bosons (weak nuclear force) are like photons, with 0 gyromagnetic ratios, or if their's is non-zero.

As you may imagine, that will be hard to measure. =) I'd say W+/- probably do, but I'm in Solid State: maybe Particle people can provide answer before moderators figure out that we are off topic and shut down the thread!

 

[Frame Dragger]

As you may imagine, that will be hard to measure. =) I'd say W+/- probably do, but I'm in Solid State: maybe Particle people can provide answer before moderators figure out that we are off topic and shut down the thread!

Whoops! Well, here's to hoping. I figured the W+/- would... the Z... *baffled look*. Then there's the question that at high energies the electroweak emerges, so really we're talking about different aspects of a potentially unified force. Now I'm confusing myself again. *groan*