My understanding of the Stern–Gerlach experiment is that neutral (0 total charge) particles are sent through a non-homogeneous magnetic field, with the expectation that the field will push that particle's path higher or lower on a detector because of the collective spin of that particle. While the detector can detect particles in a two-dimensional surface, the results of the experiment are that particles appear in only two localized areas directly above the path of the particle stream, or directly below the path of the particle stream – spin up or spin down. The conclusions from these measurements are that the particle, when measured, will always have about the same magnitude.
Why does this not follow from classical mechanical theory related to magnetism? If you shot a magnet through a similar apparatus, I would expect the magnet to be rotated to align with the magnetic field in some way which, at high enough field strengths relative to the mass of the magnet, would cause us to measure basically the same magnitude as if the magnet entered the apparatus pre-aligned with the field.
How is my explanation incorrect?
Best Answer
NOTE: this answer ignores initial angular momentum along the magnetic moment, so it isn't directly applicable to the silver atoms used in the actual Stern-Gerlach experiment. See the answer by Michael Seifert that takes angular momentum into account.
The magnet has a finite moment of inertia. What would happen when the magnet with "wrong" orientation enters Stern-Gerlach apparatus? Of course, the magnetic field will exert torque on it. The magnet starts rotating. After it comes to the equilibrium orientation, i.e. is oriented along the field, the torque is zero, but angular velocity is at maximum, and the magnet overshoots — just as in motion of usual oscillator.
If you find average magnetic moment over all the motion time, i.e. multiple periods of oscillation, you'll find that it has smaller magnitude than actual magnetic moment of the magnet. This means that net displacement in the direction of field is smaller. Now if there're lots of such identical magnets with random initial orientations, they all will have random average magnetic moment, and thus their displacement will form a continuum instead of just two points.