Consider the two-state pointer apparatus of the silver-atom experiment: an atom…
PHYSICS · Multi-part · 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
Consider the two-state pointer apparatus of the silver-atom experiment: an atom prepared in ∣ψ⟩=21(∣↑⟩+∣↓⟩) is sent through a Stern-Gerlach magnet coupled to a pointer, initially in state ∣A0⟩, such that the interaction produces ∣↑⟩∣A0⟩→∣↑⟩∣A↑⟩ and ∣↓⟩∣A0⟩→∣↓⟩∣A↓⟩ under the evolution postulate.Someone argues: 'Before any conscious observer looks at the pointer, nothing has gone wrong: the atom-plus-apparatus system is a perfectly good quantum state evolving unitarily. It is only the act of a human being looking at the pointer that forces a definite outcome to appear; that is what the measurement problem is about, and it is why we never see the apparatus itself in a superposition.'
((a)) Apply the evolution postulate to find the joint state of atom and pointer after the interaction, starting from ∣ψ⟩∣A0⟩.
((b)) Name the two postulates that are actually in tension here, and say what each predicts for the joint state.
((c)) Say what is wrong with attributing the measurement problem to the presence or absence of a conscious observer.