Quantum uncertainty

Stern-Gerlach apparatus (SGA)

Choose input state:

Spin-up
(spin 1/2) Spin-up
(spin 1)

Outcome distribution

–ħ

–ħ/2

0

ħ/2

ħ

S_θ

Quantum uncertainty: ΔS_θ = 0

Spot size due to instrumental imperfections: 0

How do quantum uncertainty, errors due to instrumental imperfections and statistical uncertainty differ from one another? Can quantum uncertainty ever be zero, and if so, under what conditions? Then go on to the Challenges tab!

Quantum uncertainty

Outcome probabilities:

Prob(+ħ/2) = 1

Prob(–ħ/2) = 0

Certain of outcome +ħ/2 prior to measurement

ΔS_θ = 0

Change quantum uncertainty: SGA angle θ = 0°

▼

Instrumental imperfections

Perfect apparatus and detector

Spread (standard deviation σ) of each spot after

many measurements: 0

Change instrumental imperfections: σ = 0

▲

Statistical uncertainty

No statistical uncertainty: infinite counts

1.000 of total counts in +ħ/2 spot (expected: 1.000)

0.000 of total counts in –ħ/2 spot (expected: 0.000)

Change statistical uncertainty: Number of counts N = ∞