Question on Stern Gerlach experiment

[Iforgot]

In the Stern Gerlach experiment, when does the electron's position get determined? Before/right after it leaves the inhomogeneous field? Or when it hits the detecting foil?

This could be tested by replacing the foil with two slits at each of the expected regions of electron incidence. If there is a diffraction pattern on the other side of the slits, that means that the electron was in a superposition of spin up and spin down states after leaving the inhomogeneous field.

 

[cesiumfrog]

Those outputs can't interfere, since you could know which slit each electron went through by measuring it's spin again. You'd need a perpendicular spin measurement first, as in a quantum eraser experiment.

 

[DrChinese]

In the Stern Gerlach experiment, when does the electron's position get determined? Before/right after it leaves the inhomogeneous field? Or when it hits the detecting foil?

This could be tested by replacing the foil with two slits at each of the expected regions of electron incidence. If there is a diffraction pattern on the other side of the slits, that means that the electron was in a superposition of spin up and spin down states after leaving the inhomogeneous field.

There are only 2 possible outputs. They are quantized as +1 and -1. There is one of the things the experiment shows.

 

[Iforgot]

Cesiumfrog,

Hehehe. To measure it's spin again, you would need another Stern Gerlach experiment after the slits. And then my questions would still be valid for that Stern Gerlach experiment.

Let me know if you know of any papers/books dealing with this question.

____________________________________________________________________
1) The Stern Gerlach experiment "measures" incident electron position on the detecting foil, not spin. We infer the spin state from the position. Are these true statements?

2) "The electron spin state is in a superposition of up and down until we see where the incident electron hit the foil". Is this a true statement?
______________________________________________________________________
Dr. Chinese,

Do you see where I'm going with this? Ideally, I would like to show that it's the periodic potential from the crystal lattice in the foil that broadens the wave function in k-space, and localizes it in r-space. This would allows us to calculate how spin transitions from a superposition of +1/-1 states, to a single state.

 

[SpectraCat]

Cesiumfrog,

Hehehe. To measure it's spin again, you would need another Stern Gerlach experiment after the slits. And then my questions would still be valid for that Stern Gerlach experiment.

Let me know if you know of any papers/books dealing with this question.

____________________________________________________________________
1) The Stern Gerlach experiment "measures" incident electron position on the detecting foil, not spin. We infer the spin state from the position. Are these true statements?

2) "The electron spin state is in a superposition of up and down until we see where the incident electron hit the foil". Is this a true statement?
______________________________________________________________________
Dr. Chinese,

Do you see where I'm going with this? Ideally, I would like to show that it's the periodic potential from the crystal lattice in the foil that broadens the wave function in k-space, and localizes it in r-space. This would allows us to calculate how spin transitions from a superposition of +1/-1 states, to a single state.

Perhaps I don't understand completely what you are proposing, but AFAICS there are several problems with your idea:

1) electrons are not amenable to Stern-Gerlach experiments, since they are charged particles, and the Lorentz force will dominate their trajectories, rather than the magnetic coupling to the spin.

2) In an S.G. experiment, the two spatial paths in the apparatus become entangled with the two values of spin, and this entanglement is resolved at the point of detection. However, if the two beams are spatially resolved, as in the historical SG experiments, then there is no ambiguity about the spin of the atoms that get deflected to a particular spot. IOW, the "upper spot" is always "spin up" and vice versa.

3) If I understood your proposed experiment, you want to put a double-slit at the end of each arm of the SG apparatus. I don't see how this will tell you much about the particle's spin ... particles passing through a physical double slit will produce an interference pattern irrespective of their spin, provided that you don't record which-path information. For this case I don't see how the spin can be correlated with which-path information, so I guess you would see interference patterns at both slits, but it wouldn't tell you anything about the question you are trying to address, i.e. whether or not the electrons were in spin-state superpositions.

 

[Iforgot]

Spectracat,

Thanks for the feed back!

3) I chose the words poorly. One slit at each arm of the SG apparatus.

2) Aha! This is what I wanted to know. Spin entanglement is resolved when the electron hits the foil!

This conversation is part of another curiosity of mine. I'm trying to understand how "measuring" "collapses" a wave-function. It just seems like words. I want to show that it can be calculated using scattering or time dependent perturbation theory formalisms.

See
https://www.physicsforums.com/showthread.php?t=399767

for the discussion

 

[Hans de Vries]

In the Stern Gerlach experiment, when does the electron's position get determined? Before/right after it leaves the inhomogeneous field? Or when it hits the detecting foil?

This could be tested by replacing the foil with two slits at each of the expected regions of electron incidence. If there is a diffraction pattern on the other side of the slits, that means that the electron was in a superposition of spin up and spin down states after leaving the inhomogeneous field.

You would need to do more as that to obtain interference.

The two states "up" and "down" do not interfere with each other just like horizontal
polarized light doesn't interfere with vertical polarized light. They are two independent
components of the electron field. You need to realign the spins to get interference.

You should get interference if the spin of the original electron is in any other direction
as those identified with "up"and "down" in the experiment. You may again compare this
with the polarization direction of light which contains both an H and a V component
dependent on the angle.

The field of the electron in the Dirac representation splits into two parts in a magnetic
field with a gradient in exactly the way as seen in Stern Gerlach experiments.


Regards, Hans

 

[Iforgot]

Ok. Just put some equivalent polarizing element in. Like they do for optics in
September 1994 / Vol. 33, No. 25 / APPLIED OPTICS