A caesium atom is prepared in the spin state along
PHYSICS · Subjective · Fermi University Physics · Quantum Mechanics · The formalism of quantum mechanics · Density matrices, open systems, entanglement and interpretation
The Structure of Quantum Mechanics, Ch The postulates, measurement and collapse
Problem
A caesium atom is prepared in the spin state ∣ψ⟩=(∣↑⟩+∣↓⟩)/2 along z. It passes through a Stern-Gerlach magnet coupled to a mechanical pointer of mass 10−9kg, initially in a state ∣A0⟩. The coupling is built so that the pointer swings left, ending in state ∣AL⟩, if the atom is deflected up, and swings right, ending in state ∣AR⟩, if the atom is deflected down. Treating atom and pointer together as an isolated system obeying the evolution postulate (P5) alone, linearity of U^(t) turns the initial pair ∣ψ⟩∣A0⟩ into the summed state
∣Ψ⟩=21(∣↑⟩∣AL⟩+∣↓⟩∣AR⟩).
In every run actually carried out, the pointer is observed to point in one direction only, never in some intermediate or double state.
(a) Using the state-reduction postulate (P4), explain why ∣Ψ⟩ cannot itself be the description of a single completed run if that run is to have a single, definite outcome.
(b) Compare the response that adds a real collapse law to P5 with the response in which only P5 acts and every branch persists, the first and third responses to the measurement problem described in this chapter. For each, state which of P4 and P5 is kept exact and which is abandoned or reinterpreted, and give one concrete question that account owes an answer to, using only the postulates and results built so far.