Curie-Weiss model of the quantum measurement process

Abstract

A Hamiltonian model is solved, which satisfies all requirements for a realistic ideal quantum measurement. The system S is a spin-1/2, whose z-component is measured through coupling with an apparatus A = M + B, consisting of a magnet M formed by a set of N ≫ 1 spins with quartic infinite-range Ising interactions, and a phonon bath B at temperature T. Initially A is in a metastable paramagnetic phase. The process involves several time-scales. Without being much affected, A first acts on S, whose state collapses in a very brief time. The mechanism differs from the usual decoherence. Soon after its irreversibility is achieved. Finally, the field induced by S on M, which may take two opposite values with probabilities given by Born's rule, drives A into its up or down ferromagnetic phase. The overall final state involves the expected correlations between the result registered in M and the state of S. The measurement is thus accounted for by standard quantum-statistical mechanics and its specific features arise from the macroscopic size of the apparatus.