Stern-Gerlach experiment with orthogonal spin detector

[msumm21]

Suppose we have a Stern-Gerlach apparatus through which we send spin-1/2 particles and subsequently measure their position. If a passing particle "collapses" to the spin up state about X, it moves "up" and is registered by detector U, otherwise it "collapses" to the spin down state about X and moves "down" and is found by detector D. Now I'm wondering if it's possible to embed the passing particles within another detector S which measures the spin about Y (orthogonal to X) without affecting the net EM field from the Stern-Gerlach magnets around the particle? So a particle along with an "attached" detector S would move through the Stern-Gerlach together. I also want to assume (1) the detector S itself has no magnetic moment (if that's possible) and (2) the detector S can be programmed to measure the spin about Y at a fixed frequency F.

If this setup is somehow feasible, I wonder what would happen when F is large? If we repeatedly measure the spin about Y I assume we must get an answer "up" or "down," but in that case it seems the spin cannot spend time in the states with spin up or down about X and hence it would go straight through the Stern-Gerlach, right? But is it possible for such a particle to go through a Stern-Gerlach detector and not "collapse" to the spin up or spin down state about X?

 

[Nugatory]

As far as quantum mechanics is concerned, the interaction that leads to a collapse must be considered instantaneous - there is no "in process" state. This is enforced by the way the mathematical formalism works: there's a "before" state, a bunch of possible "after" states, a rule (the Born rule) for calculating the probability of collapsing into one of the "after" states, but nothing about what happens in between.

Thus, your hypothetical is equivalent to performing spin measurements along different axes in rapid succession. The momentum transfer and hence the particle deflection also happens instantaneously. You could reasonably imagine that the particle is given a kick at the moment of collapse; inertia and the kicks from subsequent measurements will determine the trajectory from there.

In practice such an experiment is completely impractical because the magnetic fields from the two detectors will combine in a way that does something completely different from what you want. A more achievable thought experiment that comes to the same conclusion would use polarized photons passed through a succession of polarizing filters at different angles.