Stern-Gerlach Sequences
Sequential measurements and basis incompatibility
Send a beam of spin-1/2 particles through a sequence of Stern-Gerlach apparatuses. Choose the measurement axis (X, Y, Z) for each stage and optionally block one output. Observe how measuring along non-commuting axes randomizes the outcome of a subsequent measurement — a direct demonstration that [S_z, S_x] ≠ 0.
Input Beam
Apparatus Stages
Stage 1
Measurement Axis
Block Output
Stage 2
Measurement Axis
Block Output
Classic Experiments
Non-commuting observables cannot be simultaneously determined. Measuring spin-X after spin-Z randomizes the Z-component -- the intermediate measurement erases the prior information.