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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

SG-ZNSSG-XNS+ 75.0%blocked+ 37.5%- 37.5%37.5%37.5%sourcedetector screen

Classic Experiments

[Sz,Sx]=iSy0[S_z, S_x] = i\hbar S_y \neq 0

Non-commuting observables cannot be simultaneously determined. Measuring spin-X after spin-Z randomizes the Z-component -- the intermediate measurement erases the prior information.

Stern-Gerlach Sequences — Quantum Foundations Labs · hbar.university