Stern-Gerlach experiment - please confirm this surprising result

[Jehannum]

TL;DR

I need confirmation that something I've read is correct.

A SG device oriented along z-axis is used to prepare a stream of spin up particles from a randomised source. These are then passed through an x-axis SG device. If their spins were to be measured now they would be 50% left, 50% right. But instead, the two beams are recombined and passed through a third SG device which is z-aligned, like the first. The spins are then measured.

My expectation was that the second SG device would have randomised the spins, resulting in 50%/50% up/down but according to what I read, they will actually be measured 100% spin up. Is this correct?

 

[PeterDonis]

Summary:: I need confirmation that something I've read is correct.

We can't give that unless we see what you read, not your description of it. Can you give a reference?

 

[PeterDonis]

My expectation was that the second SG device would have randomised the spins

Not if the beams are recombined. Recombining the beams undoes what the second SG device did.

they will actually be measured 100% spin up. Is this correct?

Yes.

 

[PeroK]

Summary:: I need confirmation that something I've read is correct.

A SG device oriented along z-axis is used to prepare a stream of spin up particles from a randomised source. These are then passed through an x-axis SG device. If their spins were to be measured now they would be 50% left, 50% right. But instead, the two beams are recombined and passed through a third SG device which is z-aligned, like the first. The spins are then measured.

My expectation was that the second SG device would have randomised the spins, resulting in 50%/50% up/down but according to what I read, they will actually be measured 100% spin up. Is this correct?

There's a discussion of this here - section 6.5:

https://physics.mq.edu.au/~jcresser/Phys304/Handouts/QuantumPhysicsNotes.pdf

Despite the standard explanation of the SG experiment, a SG magnetic field does not constitute a measurement of a particle's spin. Not unless the path of the particle is subsequently measured.

 

[PeterDonis]

a SG magnetic field does not constitute a measurement of a particle's spin. Not unless the path of the particle is subsequently measured.

Yes. Another way to say this is that all the SG magnet by itself does is entangle the particle's spin with the direction of its momentum when the particle exits the magnet. Recombining the beams without any intervening measurement of momentum just undoes that entanglement.

(Note also that the usual SG experiment appears to be measuring the particle's position, not momentum, since the particle makes a dot on a detector screen. However, the location of the dot, relative to the location of the SG magnet, gives the direction of the particle's momentum when it exited the magnet. In other words, the fact that the dot's position is what is directly observed is an artifact of that particular measurement method; we could imagine other ways of measuring the direction of the particle's momentum that would be more direct, such as placing recoil detectors all around the lab that would measure the direction of recoil when the particle hit them.)

 

[vanhees71]

Summary:: I need confirmation that something I've read is correct.

A SG device oriented along z-axis is used to prepare a stream of spin up particles from a randomised source. These are then passed through an x-axis SG device. If their spins were to be measured now they would be 50% left, 50% right. But instead, the two beams are recombined and passed through a third SG device which is z-aligned, like the first. The spins are then measured.

My expectation was that the second SG device would have randomised the spins, resulting in 50%/50% up/down but according to what I read, they will actually be measured 100% spin up. Is this correct?

Can you give a reference? That's absolutely amazing, because it's an utmost tough experiment to do. Of course, as long as nothing interferes with the particles (i.e., no decoherence happens, and that's the one thing which is tough to achieve) you can in principle reverse the action of the magnetic-field of the $S_x$-measuring magnetic field, but that's the other thing which is tough in such an experiment. So I'd be highly interested to read the scientific paper about such an experiment.

 

[PeterDonis]

Can you give a reference?

I don't think anyone has actually done the "recombining beams" experiment with a SG apparatus. But the theoretical prediction is clear, and experiments such as Mach-Zehnder interferometers with photons are doing something equivalent (the second beam splitter "recombines" the beams), and those have been done many times and confirm the theoretical prediction.

 

[Fred Wright]

From the Wikipedia page on Stern-Gerlach experiment:

If we link multiple Stern–Gerlach apparatuses (the rectangles containing S-G), we can clearly see that they do not act as simple selectors, i.e. filtering out particles with one of the states (pre-existing to the measurement) and blocking the others. Instead they alter the state by observing it (as in light polarization). In the figure below, x and z name the directions of the (inhomogenous) magnetic field, with the x-z-plane being orthogonal to the particle beam. In the three S-G systems shown below, the cross-hatched squares denote the blocking of a given output, i.e. each of the S-G systems with a blocker allows only particles with one of two states to enter the next S-G apparatus in the sequence. [8]

The top illustration shows that when a second, identical, S-G apparatus is placed at the exit of the z+ beam resulting of the first apparatus, only z+ is seen in the output of the second apparatus. This result is expected since only the z+ beam from the first apparatus entered the second apparatus.

The middle system shows what happens when a different S-G apparatus is placed at the exit of the z+ beam resulting of the first apparatus, the second apparatus measuring the deflection of the beams on the x-axis instead of the z axis. The second apparatus produces x+ and x- outputs. Now classically we would expect to have one beam with the x characteristic oriented + and the z characteristic oriented +, and another with the x characteristic oriented - and the z characteristic oriented +.

The bottom system contradicts that expectation. The output of the third apparatus which measures the deflection on the z axis again shows z- as well as z+. Given that the input to the second S-G apparatus consisted only of z+, it can be inferred that a S-G apparatus must be altering the states of the particles that pass through it. This experiment can be interpreted to exhibit the uncertainty principle : since the angular momentum cannot be measured on two perpendicular directions at the same time, the measurement of the angular momentum on the x direction destroys the previous determination of the angular momentum in the z direction. That's why the third apparatus measures renewed z+ and z- beams like the x measurement really made a clean slate of the z+ output.

This seems to contradict what you claim, i.e. 100% z axis spin up.

 

[PeterDonis]

This seems to contradict what you claim

No, it doesn't. None of your cases involve recombining beams. The OP is specifically talking about recombining beams after the second (x-spin) SG measurement.

 

[vanhees71]

Of course, theoretically it's no problem to "recombine the beams" precisely such you end up at the 100% spin-up in $z$-direction, but to do a real experiment to this effect, is utmost challenging. I doubt that it can be done. There are nice papers by Scully, Schwinger et al on this issue:

https://doi.org/10.1007/BF01909939
https://ui.adsabs.harvard.edu/link_gateway/1988ZPhyD..10..135S/doi:10.1007/BF01384847
https://doi.org/10.1103/PhysRevA.40.1775

 

[Fred Wright]

No, it doesn't. None of your cases involve recombining beams. The OP is specifically talking about recombining beams after the second (x-spin) SG measurement.

Ok, my bad. I'm very interested in the recombination but unfortunately the references that vanhees71 kindly provided are behind a paywall. I wonder if in recombination, when there is no z component of magnetic field, the spin moment x-polarized particles, however, can interact with the z component of the vector potential forcing the spins into a configuration whose lowest energy state is having their z component of spin aligned to the positive z axis? Just a thought and probably wrong.

 

[PeroK]

Ok, my bad. I'm very interested in the recombination but unfortunately the references that vanhees71 kindly provided are behind a paywall. I wonder if in recombination, when there is no z component of magnetic field, the spin moment x-polarized particles, however, can interact with the z component of the vector potential forcing the spins into a configuration whose lowest energy state is having their z component of spin aligned to the positive z axis? Just a thought and probably wrong.

See the link I gave in post #4 above.

 

[Jehannum]

We can't give that unless we see what you read, not your description of it. Can you give a reference?

Sorry for the delay in replying. I sometimes have "social issues", i.e. embarrassment at having asked a stupid question and it takes me a while to pluck up the courage to peek at the replies.

The reference is a quiz question on Brilliant.org (quantum mechanics).

Edit: I got the question wrong in the quiz and it ruined my perfect score up to that point!

 

[PeterDonis]

The reference is a quiz question on Brilliant.org

Can you give a link?