Stern–Gerlach Experiment

One-Sentence Significance

The Stern–Gerlach experiment demonstrated discrete beam splitting associated with angular-momentum components in an inhomogeneous magnetic field.

What Was Measured

Neutral silver atoms passed through a nonuniform magnetic field and formed separated spots on a detector instead of a continuous smear. The field gradient couples to the magnetic moment:

$$H = - \boldsymbol\mu\cdot\mathbf B,$$

and a simplified force estimate along $z$ is

$$F_z \simeq \mu_z \frac{\partial B_z}{\partial z}.$$

In the modern spin-$1/2$ idealization, a component along direction $\hat{\mathbf n}$ has outcomes

$$S_{\hat{\mathbf n}} = \pm\frac{\hbar}{2}.$$

What It Showed

The result ruled out a simple classical picture in which magnetic moments point with a continuum of possible projections. It became a prototype for discrete quantum measurement outcomes and for the dependence of a measured spin component on apparatus orientation.

What It Did Not Show By Itself

The original experiment used silver atoms, not isolated free electrons. Its detailed interpretation involves atomic structure and magnetic moments. It is not direct evidence that a tiny classical object carries a pre-existing arrow pointing in one of two directions.

Sequential Stern–Gerlach experiments along different axes are needed to expose the noncommuting-observable lesson most cleanly.

Modern Interpretation

The experiment is modeled as a measurement of a spin or angular-momentum component. Changing the magnet orientation changes the measured operator. A state prepared as an eigenstate along one axis is generally a superposition of eigenstates along another.

The historical card points to the current glossary home for the named experiment and to the spin and measurement pages for the formalism.

Canonical Links

• Stern–Gerlach Glossary Entry
• What Spin Is
• Spin-1/2 Hilbert Space
• Pauli Matrices
• Stern–Gerlach Revisited
• Projective Measurement
• Sequential Measurements

Common Myths

• The spots reveal pre-existing classical spin directions.
• The original experiment is exactly a free-electron spin measurement.
• A Stern–Gerlach device measures “spin” without specifying an axis.
• Real apparatus details are irrelevant to the historical experiment.

Quick Check

Why does rotating the magnet change the measured observable?

Solution

The field gradient defines the spatial direction whose magnetic-moment component couples to the apparatus. Rotating the magnet changes that direction, so the idealized measurement changes from one spin-component operator to another.

References

• W. Gerlach and O. Stern, “Der experimentelle Nachweis der Richtungsquantelung im Magnetfeld,” Zeitschrift fuer Physik 9, 349-352, 1922.
• B. Friedrich and D. Herschbach, “Stern and Gerlach: How a Bad Cigar Helped Reorient Atomic Physics,” Physics Today 56, 53-59, 2003.
• J. J. Sakurai and J. Napolitano, Modern Quantum Mechanics, 3rd ed., Cambridge University Press, 2020.