Stern-Gerlach experiment
In 1922 Otto Stern and Walther Gerlach sent a beam of silver atoms through a cleverly shaped, uneven magnetic field and let it strike a glass plate. A magnet placed in such a field feels a sideways push, and an atom acts like a tiny magnet because of the angular momentum of its electrons. The amount of deflection should report how that little magnet is tilted relative to the field.
Classical physics made a clear prediction: the atoms' magnets should point every which way, so the beam should smear out into a continuous vertical streak. Instead the beam split cleanly into just two spots, one deflected up and one down, with nothing in between. The tilt of the atomic magnet was not free to take any value; it was quantized, allowed only two settings along the chosen direction.
Though Stern and Gerlach were probing magnetism, what they had actually caught was electron spin, before spin had even been named. The experiment is now the textbook demonstration that a quantum measurement of a spin-½ system yields one of exactly two outcomes, and it remains a touchstone for explaining how measurement, superposition, and quantization work.
A continuous smear was expected; two discrete spots appeared, revealing quantized spin.
The two spots are not the atom 'choosing' between two pre-existing orientations. Before measurement the spin can be in a superposition; the device forces one of two results, with probabilities set by the prior state.