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Lets define experiment as following (excuse me my bad English, please):

- vibrating bath with non-conductive, non-magnetic, non-paramagnetic, non-diamagnetic fluid;

- vibrating bath is wide enough to avoid excessive interference with reflected waves from bath sides;

- vibrating bath has regular pattern on top of fluid, without any irregularities in space of experiment;

- small charged droplets of fluid on top of bath;

- north and south poles of a magnet are placed horizontally, without touching of bath fluid or droplets, e.g. at sides of bath, OR over fluid, OR under bath;

- an apparatus creates droplets of same size with random spin in all 3 dimensions;

- droplets are forced to walk through the batch, starting at center line between north and south pole and following that line;

- without magnetic field applied, droplets must walk straight;

- an detectors to measure decline of droplet path from center line must be installed at end of magnetic pole.

I expect that, when magnetic field is applied, droplets will slide completely to left or completely to the right, like electrons in Stern-Gerlach experiment.

It's not a quantum experiment, of course, but it can provide insight on nature of quantum spin.

PS.

Sorry, droplets must be charged, not magnetic. Updated.




The main point of the Stern-Gerlach experiment was that the electrons hitting the screen were forming two distinct dots instead of a long spread out line, therefore proving that the angular momentum is quantised. In your example you will instead have simply a spread-out distribution because there is no quantisation of the angular momentum of your droplets.

The pilot wave usually refers to the spatial degrees of freedom, especially in these classical mock-ups with balls on top of waves. They do not properly addressed internal degrees of freedom like spin.

Unrelated to those macroscopic mock-ups, pilot wave theory actually has serious problems with the description of anything that is not a spatial degree of freedom.

You can still use pilot wave theory to describe the quantum behavior of the coordinates of a particle. But even then, the classical mock-ups we are discussing will not show anything inherently quantum - it will simply produce some interference patterns, that can be explained classically.

P.S. side note: An important part in the Stern-Gerlach experiment was that the magnetic field was not homogeneous, because it is the gradient of the field, not the field itself that causes the electrons to move.


IMHO, Stern-Gerlach experiment demonstrates interaction of magnet field with guiding wave mediated via particle, so I expect that magnet will steer particle-wave into same spots, thus will demonstrate «quantum» behavior of particle spin at macro level.


Without disrespect I insist that you are wrong about that. The spin degree of freedom is "internal", unrelated to the position of the particle. The pilot wave does not influence that spin, and if you have a big ball on top of a wave, that wave does not care about the angular momentum of the ball. The ball is big and classical, hence its angular momentum is (practically) not quantized.

The thread got a bit long, but if you are really interested in learning about this I would be happy to continue the discussion through email (stefan.krastanov@yale.edu). You probably also need proof of some kind of qualification on my part - my online profile does prove that I work at a respected institute doing research on that topic.




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