Effect of changes in Stern-Gerlach fields

[bunburryist]

In regard to the Stern-Gerlach experiment, what happens if the field starts out homogenous or very weak, and is slowly changed to the strong inhomogenous field described in the experiment?
There are two versions of this, what might be called “transition period” question. One would be . . .
A. If the field starts out full strength, but homogenous, and then the geometry is slowly altered, when do the atoms react to the field and exhibit measured changes in their spin orientation?
B. If the field starts out very weak, but inhomogenous, and then is increased in strength, when do the atoms react to the field and exhibit measured changes in their spin orientation?

My guess would be that the probabilistic nature of quantum physics would show itself in this way as well. I would think that as the geometry of the field is altered (A) or as the strength of the altered field is increased (B), at first almost none of the atoms would react, but as the changes became more exaggerated, a larger and larger proportion of the atoms would react to the field, until the fields are altered to the point where all the atoms react.

In this “transition period,” would the speed at which the atoms passed through the field have an impact of the number of atoms reacting to the field? If the field is very weak (so that only a fraction of the atoms responded to the field, would there be are a higher number reacting if the atoms were passing through the field slowly (spending more time in the field) than if they passed through the field quickly?

 

[Vanadium 50]

The atoms always react to the field. The size of the response is proportional to the strength of the field.

 

[bunburryist]

Perhaps I should have been more exact in my question. My question is not about the movement of an atom in a magnetic field, but rather about measurement of the atoms spin orientation relative to the magnetic field.
Let me introduce the idea I’m trying to get at by talking first about an experiment where we are trying to measure the spin orientation of a free electron in a magnetic field. We prepare it so that it’s spin axis is pointing what will be north when the magnetic field is turned on. (It will flip and point south.) It will have a probability of 1 that it will flip. It will not “flip” instantly, but rather will do so within some half-life time frame which is determined by the strength of the magnetic field. The weaker the field, the longer the half-life. For an explanation of this, go to lecture 2 of the Stanford University lecture on quantum entanglement.
http://www.youtube.com/watch?v=VtBRKw1Ab7E&feature=PlayList&p=F049C87F35C3A8D3&index=2
at time27:27 – 28:40.
If the magnetic field is sufficiently weak, the electron will have a relatively long spin-flip half life (I don’t know the proper terminology). If we have a field strength so that the spin-flip half life is 1 minute, and we pass the electron through the field for one minute, it will have a 50/50 chance of flipping in that time.
Now let’s go back to the Stern-Gerlach experiment. Does an atom passing through a Stern-Gerlach apparatus have a similar or analogous spin flip half-life? Suppose that instead of having a set-up where the field is strong and every atoms spin is measured as pointing “up” or “down,” let’s make it weak – weak enough so that it’s spin flip half-live is long; long enough that the time the atom spends in the magnetic field is only long enough that each atom has only a 50% chance of reacting to the field. We prepare the atom so that it’s spin orientation is such that it would have a 50% chance of going toward the + or – part of the field. If the field is weak enough, is there a chance that the silver atom will pass through without reacting to the field? Will it behave as if it had gone through no field at all?
My questions -
A. If the field starts out full strength, but homogenous, and then the geometry is slowly altered, when do the atoms react to the field and exhibit measured changes in their spin orientation?
B. If the field starts out very weak, but inhomogenous, and then is increased in strength, when do the atoms react to the field and exhibit measured changes in their spin orientation?
- may be better expressed as -
Is the electron spin-flip half-live concept relevant in the case of the silver atoms spin orientation, and -
will the half-life decrease as the field strength is increased?