Physics

Stern-Gerlach Experiment

Send silver atoms through a magnet whose field is stronger on one side than the other. Classically the beam should smear into a band. It arrives as two spots. Chain the analysers, turn the next one, and the atoms keep giving the same two answers while forgetting the answer they gave before.

Each analyser passes one of its two beams on and stops the other; the cards compare what the last one measured with what the angle predicts

Upper spot—

—

Setup

Analyser 1 axis 0°

Beam kept after 1

Analyser 2 axis 90°

Beam kept after 2

Analyser 3 axis 0°

Beam intensity 24/s

Show what classical physics predicts

Atoms detected—

Upper spot—

Lower spot—

cos²(Δ/2) says—

What to observe

One analyser: a classical moment could point any way, so the beam should smear into a band. It lands as two spots, because spin along any axis is only ever ±ħ/2.
Two analysers on the same axis: the lower spot stays empty. A measurement is repeatable, it leaves the atom in the state it reported.
Turn analyser 2 away from z and the split follows cos²(Δ/2): 75% up at 60°, an even split at 90°. Half-angles are the fingerprint of spin ½.
z, x, z: the atoms were all up along z, yet the third analyser splits them 50/50. Measuring x erased what was known about z.

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