The Zeeman effect and Stern-Gerlach experiment

Without a magnetic field, states that share the same orbital quantum number but differ in magnetic quantum number all have the same energy — there is nothing in the atom's environment to distinguish "pointing this way" from "pointing that way." Switch on a magnetic field and that symmetry breaks: each magnetic quantum number now corresponds to a slightly different energy, because the atom's magnetic moment interacts with the field differently depending on its orientation. A single spectral line, which used to come from one transition, now splits into several closely spaced lines — one for each allowed change in magnetic quantum number.

The Stern-Gerlach experiment pushed this further and asked a sharper question: is that splitting continuous, the way a classical compass needle settles at any angle, or quantized into a small number of discrete values? Silver atoms, chosen because their ground state has zero net orbital angular momentum, were sent through a strongly non-uniform magnetic field and onto a detector screen. If magnetic moments could point any which way, the beam should have smeared into a single broad band. Instead it split cleanly into two spots.

That result could not be explained by orbital motion at all, since the atoms had none in their ground state. What it revealed was spin: an intrinsic form of angular momentum every electron carries, with exactly two possible orientations relative to any measurement axis, entirely independent of how the electron is moving through space.