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Sandbox Physics

Q003 · Spin / sequential measurement

Stern–Gerlach Sequence

Prepare a neutral spin-half beam, rotate the middle magnet, and select a channel or ignore its result. Follow the retained and blocked ports into the final analyzer, then compare raw counts with a bypass experiment.

Interactive modelStern–Gerlach Sequence
Model positive probability—\text{—}
Positive / negative / rejected—\text{—}
Current-setting trials—\text{—}
Acquired positive fraction—\text{—}
95% Wilson interval—\text{—}
Output-state purity—\text{—}
Model acceptance—\text{—}
Physical deflection before magnification—\text{—}

SIMULATED ACQUISITION

Make a prediction. Collect the evidence.

No acquired record yet.

Inference from acquired counts

Acquire a scan to estimate the signal.

—\text{—}
Density matrix and count conventions
ρ=I+r⋅σ2\rho=\frac{I+\boldsymbol r\cdot\boldsymbol\sigma}{2}

Latest raw events · full record in CSV
EventSettingOutcome

Scientific basis: Feynman III.6 · MIT 8.05 · NIST Ramsey

Physics tutorial

What a middle analyzer changes

BackgroundA neutral beam couples its magnetic moment to a gradient. The separated ports carry different spin projections.

Why it mattersSequences of spin filters distinguish repeatable outcomes, incompatible measurements and postselection losses.

Start with the essentials

Focus question
Does ignoring a middle result leave the input spin unchanged?
One-sentence intuition
The unread instrument removes coherence between its ports. Bypassing it preserves coherence.

Core mathematical model

Adjacent spin filters

P(b∣a)=(1+ab nA⋅nB)/2P(b|a)=(1+ab\,\boldsymbol n_A\cdot\boldsymbol n_B)/2

Adjacent spin filters

Unread measurement is dephasing, not a bypass

ρunread=∑b=±ΠbρΠb\rho_{\rm unread}=\sum_{b=\pm}\Pi_b\rho\Pi_b

Unread measurement is dephasing, not a bypass

Constant-gradient paraxial deflection before display magnification

d=μGmv2L(D+L/2)d=\frac{\mu G}{mv^2}L(D+L/2)

Constant-gradient paraxial deflection before display magnification

Common difficulties

Conditional counts can conceal losses

Typical misconceptionHalf the transmitted beam means half the original input.

Better mental modelAt crossed selected filters, one quarter of the prepared input reaches the final positive port. Rejected counts must remain in the unconditional denominator.

A uniform field is not a splitter

Typical misconceptionA uniform magnetic field alone separates this neutral beam.

Better mental modelA gradient supplies force. Uniform fields can precess spin; their complete beam dynamics are outside this ideal projector model.

Run the experiment

  1. 01

    Repeat an axis

    Choose Same axis and acquire shots.

    What to observe: Every prepared positive input exits the positive final port.
  2. 02

    Cross the middle axis

    Choose Crossed filters and acquire shots. Predict all three count bins first.

    What to observe: Half the prepared input is rejected; a quarter reaches each final port on average.
  3. 03

    Ignore instead of select

    Choose Unread middle, acquire, then compare with Bypass middle.

    What to observe: Unread gives equal final probabilities. Bypass returns the original positive state. The schematic relays retain distinguishable paths.
  4. 04

    Rotate and inspect

    Drag the middle axis, acquire an angle scan and inspect overview, side and final collector.

    What to observe: Port separation follows the actual gradient direction. Gradient magnitude changes displacement, while ideal spin overlap depends only on relative axes.