The Stern-Gerlach experiment

How to "see" spin

Spin would be a pure abstraction if it had no measurable consequence. The Stern-Gerlach experiment (1922) gives the most direct and spectacular proof of it: it reveals, to the eye, the quantization of spin.

The setup

A beam of atoms (originally silver) is sent through a non-uniform magnetic field, and one then looks at where they strike a screen. Since each atom carries a magnetic moment linked to the spin of its electron, the field deflects it.

       aimant (champ non uniforme)
        _______________
       |    N          |
   ----|-->            |----> ecran
   faisceau            |
   d'atomes            |
       |_______________|
            S

What we would expect classically

If spin were a classical quantity (a small needle able to point in any direction), the atoms would be deflected in every possible way, according to the random orientation of their needle. One would obtain a continuous spot spread across the screen:

   Prediction classique :          Ecran
                                    |####|   <- une bande continue
                                    |####|      (toutes les deviations)
                                    |####|

What we observe

Instead, the beam splits into two sharp spots, one deflected upward, the other downward, with nothing in between:

   Observation reelle :            Ecran
                                    | ##      <- spin "up"   (+1/2)
                                    |
                                    |         <- RIEN au milieu
                                    |
                                    | ##      <- spin "down" (-1/2)

Spin can take only two values: there is no intermediate orientation. This is the quantization of spin, made visible. The quantity does not vary continuously; it "jumps" between two values, exactly as the energy levels jump from one rung to another.

The mystery of successive measurements

Stern-Gerlach conceals a subtlety that unveils the nature of quantum measurement. Take the "up" beam that came out of a first apparatus, and send it through again:

   1) appareil vertical -> on garde SEULEMENT le faisceau "up"

   2) ce faisceau "up" dans un 2e appareil VERTICAL
      -> 100 % "up"   (coherent : il etait deja up)

   3) ce faisceau "up" dans un appareil HORIZONTAL
      -> 50 % "gauche", 50 % "droite"  (il "oublie" son up !)

   4) on reprend la sortie "gauche", on remet un appareil VERTICAL
      -> re-50 % up, 50 % down   (le "up" initial est PERDU !)

Measuring the horizontal spin destroys the information about the vertical spin. One cannot know both at once: it is a manifestation of the uncertainty principle applied to spin. The measurement does not reveal a pre-existing value, it forces the system to adopt one, erasing the other.

In summary

The Stern-Gerlach experiment sends atoms into a non-uniform magnetic field: instead of a continuous spot (expected classically), the beam splits into two sharp spots, proving that spin is quantized (up or down, nothing in between). Successive measurements along different directions show, moreover, that measuring one component of the spin destroys the information about another — the measurement creates the result rather than revealing it.