Lab · Cascaded Stern–Gerlach: recombination

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Five machines: the first (1) selects the state m₀=+k, the three central ones (2·3·4) split it (into m₉₀=+k and m₉₀=−k) and recombine it, the last (5) measures m₀ again. Open and close the gates on the two branches (click on the drawing) and fill in the truth table.

Truth table · P(m₀=−k)● INTERF.

+k gate	−k gate	P(m₀=−k)
open	closed	?
closed	open	?
open	open	?
closed	closed	?

Decomposition:|m₀=+k⟩ = (1/√2)|m₉₀=+k⟩ + (1/√2)|m₉₀=−k⟩

Case:

Measuring m₀:

Each branch alone gives P(m₀=−k)=50%. One would think opening both branches adds up to 100%: instead it cancels to 0% (|m₀=+k⟩ is rebuilt). Blocking both branches, obviously, lets nothing through: 0%.

50% + 50% → 0%: amplitudes add, not probabilities.

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La Quantistica · Local lab · Ch. 11F. Palma

Simulated laboratory, written in 2026 together with GitHub Copilot: a teaching model, not scientific software.