Angular momentum and spin

Equipment

• Beam model through the inhomogeneous Stern–Gerlach magnet
• Measurement-axis angle θ and beam-count sliders
• Two-spot +/− counter display and sequential-measurement panel 2

Procedure

1. Two spots instead of a smear

   Set θ = 0 and «Beam count» ~120: watch the beam split into exactly two spots instead of a continuous smear. This evidences spin quantization: only two measurable values $\pm\hbar/2$ — an intrinsic electron property, not classical rotation.

2. Rotate the measurement axis

   Drag «Measurement axis θ» from 0° to 180°: the spots don't slide continuously — the particle fractions in the two spots change. Tally the split at θ = 60°, 90°, 120°; for an initial spin-up along z, verify $P_{+}(\theta)=\cos^2(\theta/2)$ — 75% at 60°, 50% at 90°, 25% at 120%.

3. Sequential measurement erases state

   In panel 2, watch particles traverse two SG magnets in series along different axes (z then x). The first measurement filters spin-z; the second, along x, «forgets» the z result — the split returns to 50/50: two non-commuting observables ($[S_x,S_z]\ne0$) cannot be sharp simultaneously.

4. Statistics and prediction

   Raise «Beam count» to 300 at θ = 90°: statistical fluctuation around 50/50 shrinks as $\sim1/\sqrt{N}$. Predict the fraction at θ = 45° ($\cos^2 22.5°\approx 0.85$) before measuring, check, then argue why one cannot «peek» at a spin direction without disturbing it — the foundation of quantum cryptography.

Simulation

Experiment history

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