Experiment #21 · Scientific experiment

The Stern–Gerlach Experiment

Spin quantisation and the discreteness of measurement

Otto Stern and Walther Gerlach · 1922 · Quantum mechanics

First published: O. Stern & W. Gerlach, "Der experimentelle Nachweis der Richtungsquantelung im Magnetfeld", *Zeitschrift für Physik* 9 (1922): 349–352.

Silver atoms passed through an inhomogeneous magnetic field split into two discrete beams — not a continuous distribution. Angular momentum is quantised.

A beam of silver atoms is passed through a strongly inhomogeneous magnetic field. Classically, the magnetic moments are distributed continuously, and the beam should spread out into a smear. Instead, the beam splits cleanly into two — corresponding to spin up and spin down along the magnetic axis. The discreteness of the outcomes is the first unambiguous demonstration of quantum-mechanical quantisation of angular momentum, and it remains the cleanest experimental introduction to the projection postulate. Subsequent variants (sequential analysers along different axes) demonstrated the non-commutativity of spin measurements — the empirical heart of quantum incompatibility.

Formulation

Source → collimator → inhomogeneous magnetic field (gradient along z) → screen. Classical prediction: continuous distribution. Observed: two discrete spots at ±½ℏ. Subsequent two-stage variants show that measurement along x after measurement along z destroys z-information — observables in different directions do not commute.

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Dimensions Engaged

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Matter

Forces Matter · Conservation and Ontological Status to incorporate intrinsic discrete properties (spin) that have no classical analogue.

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Observer

Engages Observer · Metaphysical Agency: the choice of measurement axis is constitutive of which property is definite. Different choices yield genuinely incompatible descriptions.

Responses — How Schools Engage

Affirms / takes the bait 4

Quantum Realism

The cleanest possible demonstration that nature is fundamentally quantised. Spin is not a hidden classical angular momentum but a structurally distinct property with no continuous shadow.

Naturalism

A canonical case of an experiment forcing revision of classical concepts: the observed discreteness cannot be reconciled with continuous classical physics. Quantum mechanics is empirically mandated.

Structuralism

Spin is the cleanest example of an ontological property that is purely structural — defined by its commutation relations, with no intrinsic "what it is" to bear them.

Logical Positivism

A model case for treating operational discreteness as constitutive: there is no further fact about the silver atom's magnetic moment beyond what the detector registers.

Reframes the question 2

Realism

Realists about quantum properties accept the empirical discreteness while debating whether the property is intrinsic to the atom prior to measurement (hidden-variable readings) or only co-created by the measurement context (contextualism).

Pragmatism

The experiment teaches us how to do quantum experiments — pragmatically, that is what spin *is*: a thing measurable in this way, with these statistics. Metaphysical glosses come second.