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Physics, Astronomy & Cosmology / How many spots are produced from Stern-Gerlach apparatus that rotates?
« on: 15/03/2024 15:01:23 »
Hi.
Hopefully, some of you have heard of Stern-Gerlach apparatus.
Image taken from: https://en.wikipedia.org/wiki/Stern%E2%80%93Gerlach_experiment where some more information is also avaialble.
Basically, we could send some electrons through a piece of Stern-Gerlach apparatus aligned in the z-axis direction and they would have their path deflected up or down dependng on whether they have a z-component of spin +1/2 or -1/2. We only end up with two spots or locations on the screen rather than a smeared out line - suggesting that this spin is quantised. I expect you've seen or heard the usual explanations.
Similarly we could turn the appratus sideways, so that the magnetic field is aligned in the y-axis. Then we have two spots separated left and right instead of up and down.
More interestingly we can send the electrons through a z-axis aligned apparatus and then send them through a y-axis aligned apparatus. What we find is that electrons with the z-component of spin +1/2 will still have an equal chance of having the y-component of their spin reported as being + or - 1/2 when it is measured. Overall, we end up with four spots or locations for the electrons at the end with an equal intensity on the screen: 1/4 went up and left, 1/4 went up and right, 1/4 down and left, 1/4 down and right.
If you were able to trace the path of an electron throughout the whole experiment then you expect to observe electrons that were near the North magnetic pole of the first apparatus to be deflected left or right with equal probaility in the second apparatus. Similarly, those near the South pole of the first apparatus were deflected left or right with equal probability in the second appratus. At the end of the experiment then, the electrons near the North pole of the last appartus were not necessarily near the North pole of the first appartus, they could have come from the South pole in the first apparatus. I hope this makes sense, even if you need to read it twice. The electrons can move in the two directions independantly in both pieces of apparatus. Those which are on the Left in the final apparatus could have had a total movement that was Up then Left or Down then Left.
Now, what happens if you do the experiment slightly differently? Instead of having two pieces of apparatus, with one just in front of the other, we will use just one very long Stern-Gerlach apparatus and slowly rotate the apparatus while the electrons are travelling through it. Initially the apparatus would be aligned in z-axis direction when the electrons enter it, it would then be rotated so that the magnetic field was aligned in the y-axis direction by the time the electrons exit from it.
You would expect the electrons to get deflected according to their spin as usual. What path will the electrons actually take now? If an electron had started to move toward the North pole of the appartus when it entered the apparatus, that means it had z-component of spin +1/2. In principle it can still have a y-component of spin that is + or -1/2 as shown in the original experiment, which could suggest it will move away from the North pole and toward the South pole of the apparatus when the apparatus is rotated and now measuring the y-component of spin.
On the other hand, perhaps it ALWAYS stays near the North pole of the apparatus even during the rotation. Will we only get two spots on the screen when the electrons exit the apparatus? If it's still just the usual four spots on the screen, then you've got to ask yourself some questions: Will some electrons that were at the North pole initially or early on, move to the south pole later in the experiment, while an equal number that were at the South pole move to the North pole? (i.e. so you may have equal total numbers at the North and South poles of the apparatus but some electrons have switched sides during the experiment?)
I honestly don't know what we will get and would like some opinions. I suspect we are only going to get two spots on the screen at the end and the situation will be similar to sending polarised light through polarising filters. (Birefly recall experiments where polarised light is sent into a polarising filter. If you use one polarising filter at 90 degrees to the incoming light, then you get nothing through. If you use two polarising filters, the first at 45 degrees orientation to the incoming light, the second at 45 degrees to the first (so now a total of 90 degrees to the original light) then you do get some light through at the end. The more filters you add and the more gradually you ask the photons questions about the orientation of their polaristaion, then the more light will be passed through at the end).
Best Wishes.
Hopefully, some of you have heard of Stern-Gerlach apparatus.
Image taken from: https://en.wikipedia.org/wiki/Stern%E2%80%93Gerlach_experiment where some more information is also avaialble.
Basically, we could send some electrons through a piece of Stern-Gerlach apparatus aligned in the z-axis direction and they would have their path deflected up or down dependng on whether they have a z-component of spin +1/2 or -1/2. We only end up with two spots or locations on the screen rather than a smeared out line - suggesting that this spin is quantised. I expect you've seen or heard the usual explanations.
Similarly we could turn the appratus sideways, so that the magnetic field is aligned in the y-axis. Then we have two spots separated left and right instead of up and down.
More interestingly we can send the electrons through a z-axis aligned apparatus and then send them through a y-axis aligned apparatus. What we find is that electrons with the z-component of spin +1/2 will still have an equal chance of having the y-component of their spin reported as being + or - 1/2 when it is measured. Overall, we end up with four spots or locations for the electrons at the end with an equal intensity on the screen: 1/4 went up and left, 1/4 went up and right, 1/4 down and left, 1/4 down and right.
If you were able to trace the path of an electron throughout the whole experiment then you expect to observe electrons that were near the North magnetic pole of the first apparatus to be deflected left or right with equal probaility in the second apparatus. Similarly, those near the South pole of the first apparatus were deflected left or right with equal probability in the second appratus. At the end of the experiment then, the electrons near the North pole of the last appartus were not necessarily near the North pole of the first appartus, they could have come from the South pole in the first apparatus. I hope this makes sense, even if you need to read it twice. The electrons can move in the two directions independantly in both pieces of apparatus. Those which are on the Left in the final apparatus could have had a total movement that was Up then Left or Down then Left.
Now, what happens if you do the experiment slightly differently? Instead of having two pieces of apparatus, with one just in front of the other, we will use just one very long Stern-Gerlach apparatus and slowly rotate the apparatus while the electrons are travelling through it. Initially the apparatus would be aligned in z-axis direction when the electrons enter it, it would then be rotated so that the magnetic field was aligned in the y-axis direction by the time the electrons exit from it.
You would expect the electrons to get deflected according to their spin as usual. What path will the electrons actually take now? If an electron had started to move toward the North pole of the appartus when it entered the apparatus, that means it had z-component of spin +1/2. In principle it can still have a y-component of spin that is + or -1/2 as shown in the original experiment, which could suggest it will move away from the North pole and toward the South pole of the apparatus when the apparatus is rotated and now measuring the y-component of spin.
On the other hand, perhaps it ALWAYS stays near the North pole of the apparatus even during the rotation. Will we only get two spots on the screen when the electrons exit the apparatus? If it's still just the usual four spots on the screen, then you've got to ask yourself some questions: Will some electrons that were at the North pole initially or early on, move to the south pole later in the experiment, while an equal number that were at the South pole move to the North pole? (i.e. so you may have equal total numbers at the North and South poles of the apparatus but some electrons have switched sides during the experiment?)
I honestly don't know what we will get and would like some opinions. I suspect we are only going to get two spots on the screen at the end and the situation will be similar to sending polarised light through polarising filters. (Birefly recall experiments where polarised light is sent into a polarising filter. If you use one polarising filter at 90 degrees to the incoming light, then you get nothing through. If you use two polarising filters, the first at 45 degrees orientation to the incoming light, the second at 45 degrees to the first (so now a total of 90 degrees to the original light) then you do get some light through at the end. The more filters you add and the more gradually you ask the photons questions about the orientation of their polaristaion, then the more light will be passed through at the end).
Best Wishes.