Stern-Gerlach w. normal distribution if magnets were more separated?

[ndvcxk123]

TL;DR Summary

Experim. conditions in Stern-Gerlach

Just wondered if the power of mags. is decreased, or they are more separated, don't you get a normal distribution ? (I'm in biology) - would you also not have predicted that w. reasonably strong magnets, they will either end one one side or the other ? Thx a lot!

 

[romsofia]

Here is program written up to do some "virtual" stern gerlach experiments, you can add magnets with varying strength, and see the outcome for yourself: http://sites.science.oregonstate.edu/~mcintyre/ph425/spins/index.html

 

[Nugatory]

Just wondered if the power of mags. is decreased...

When you read a description of the experiment in a textbook, you are getting an idealized description - the only relevant forces are from the inhomogeneous magnetic field and everything else (your particle source won’t be emitting every particle on an exactly straight path, some of the particles will collide with stray air molecules wandering through, your magnets won’t be perfectly aligned and the power supply won’t be perfectly stable, your detectors will generate occasional false positives or even true positives from other stray particles, ...) is being ignored. If the magnetic field is strong enough to overwhelm all these sources of error, then this is a good approximation.

But as the magnetic field becomes weaker relative to everything else, the effect that we’re looking for becomes less obvious and stands out less from all this random stuff that’s going on. So the quick answer to your question is yes - if these error sources are randomly distributed, as weaken the magnetic field we’ll get something that looks more Gaussian and less like the neat two-dot picture in the books.

Experimental physics is a lot harder than it sounds when you read about it. Experimentalists need a strong background in statistics so that they have the tools to separate real effects from random noise, serious papers will always include error bars in the conclusions, and experiments are carefully designed to minimize random noise.

 

[vanhees71]

One should however keep in mind that a strong homogeneous piece of the magnetic field in the direction of the to-be-measured/determined spin determined is crucial too: It makes the spin rapidly precede around the so chosen direction and thus only the spin component in this direction is relevant for the deflection due to the force on the dipole moment via the gradient of the magnetic field. Only this justifies the idealized description of the experiment in the textbooks.

 

[PeroK]

Summary:: Experim. conditions in Stern-Gerlach

Just wondered if the power of mags. is decreased, or they are more separated, don't you get a normal distribution ? (I'm in biology) - would you also not have predicted that w. reasonably strong magnets, they will either end one one side or the other ? Thx a lot!

I think your question is: doesn't classical electromagnetism predict the SG result for a sufficiently strong magnetic field?

The answer is no. The deflection is due to the electron's magnetic dipole moment, not the Coulomb force for a charged particle. The deflection, classically, should vary continuously with random electron spin orientations.

One of the difficulties in doing the SG experiment is to control the potentially large Coulomb force to reveal the deflection due to the magnetic dipole moment.

 

[vanhees71]

Well, that's why the SGE is usually done with uncharged "particles" (originally in 1922 in Frankfurt with Ag atoms). Bohr has quite quickly shown that it's practically impossible to do with free electrons. For the very interesting history, see

https://link.springer.com/article/10.1140/epjh/e2016-70053-2