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A small quantum scattering system (the microsystem) is studied in interactionwith a large system (the macrosystem) described by unknown stochasticvariables. The interaction between the two systems is diagonal for themicrosystem in a certain orthonormal basis, and the interaction gives animprint on the macrosystem. Moreover, the interaction is assumed to involveonly small transfers of energy and momentum between the two systems (ascompared to typical energies/momenta within the microsystem). The analysis iscarried out within scattering theory. Calculated in the conventional way, thetransition amplitude for the whole system factorizes. The interaction takingplace within the macrosystem is assumed to depend on the stochastic variablesin such a way that, on the average, no particular basis vector state of themicrosystem is favoured. The density matrix is studied in a formalism whichincludes generation of the ingoing state and absorption of the final state.Then the dependence of the final state on the conventional scattering amplitudefor the microsystem is highly non-linear.  In the thermodynamic limit of the macrosystem, the density matrix of theensemble (of microsystem plus macrosystem) develops into a final state whichinvolves a set of macroscopically distinguishable states, each with themicrosystem in one of the basis vector states and the macrosystem in anentangled state.  For an element of the ensemble, i.e., for a single measurement, the result isinstead a random walk, where the microsystem ends up in one of the basis vectorstates (reduction of the wave packet).

Quantum Measurement as a Final-State Interaction with a Macroscopic External System