Multiple spin measurements in the same direction What will be the outcome of the experiment during which charged particles will go through the set of Stern Gerlach apparatus aligned in the same direction (say Up)?
                         [SG Up] < ?1   
 [ Source ] -> [SG Up] <
                         [SG Up] < ?2

Has been this experiment actually conducted? What was its outcome?

*

*for 1 "all up"

*for 2 "all down"

or something else?
 A: The Stern-Gerlach apparatus creates what is known as spin-path entanglement – ie. the particle's spin and its position become entangled. More specifically, if a particle flies from a SG apparatus up, then we are sure that its spin is also up, and vice versa.
If we measure spin along an axis and the incoming particle is already “polarized” along the same axis, we will get just one result with 100 % probability. The reason for this is simple: assume a particle's spin points along an axis $\vec s$ and the SG apparatus has an axis $\vec a$, then the probability of measuring “up” is given by $\cos^2 \frac{\alpha}{2}$, where $\alpha$ is the angle between $\vec s$ and $\vec a$. For $\alpha = 0$ the probability is $1$ and for $\alpha = 180^°$ the probability is $0$.

Therefore, your intuition is right. Since all the particles ariving at detector 1 are spin up, they will all bend upwards. Likewise, all the particles ariving at 2 are all spin down, therefore they'd be deflected down. If your source is giving off “unpolarized” particles with spin directed in random directions, then you'd get a 50-50 chance of measuring “1 up” and “2 down”.

But as @Charlie pointed out, this applies to “fast” consecutive measurements, ie. those where you don't apply any additional tricks to the flying particles. For example, if there was an additional homogeneous magnetic field between the SG apparatuses, then the Larmor precession would steer the spins away from the perfect zero angle and you could measure “1 down” and “2 up” with non-zero probability.
