Measuring magnetic projections

What does the previous chapter have to do with quantum mechanics? I have said that the predictions of quantum mechanics are significantly different from those of classical mechanics only when applied to very small objects. How could we make such a tiny compass needle? In fact we don't need to make one, because nature itself supplies one. It is natural to suppose that an atom acts like a tiny magnetic needle because its orbiting electron mimics a current loop.

In 1922, physicists Otto Stern and Walther Gerlach decided to test this supposition by measuring the magnetic arrow associated with a silver atom. It is clear that they could not do this by watching an individual atom precess in a uniform magnetic field! Instead, they injected a moving silver atom into a non-uniform field and noticed how the resulting force pushed the atom around. The “Stern–Gerlach apparatus” sketched on the next page thus measures the projection of an atom's magnetic arrow on the vertical axis.

What results would you expect from this experiment? Think about this for a moment before reading on.

Classical expectations

I don't know about you, but here is what I would expect: Once the atom enters the non-uniform magnetic field, its magnetic arrow precesses in such a way that its projection on the vertical axis remains constant. While this precession is taking place, there is also a force on the atom, and the magnitude of that force depends upon the value of the projection. If the atom has a large positive projection, it will experience a large upward force and move up sharply.