An approach to the Copenhagen interpretation of quantum mechanics is developed which makes the Heisenberg cut between the deterministic microscopic quantum world and the stochastic macroscopic world explicit. The stochastic nature of quantum mechanics arises when the system is probed by a set of coarse-grained macroscopic observables whose resolution scale defines the Heisenberg cut. From the point of view of these observables, the system lies in a quantum microstate drawn from a set that depends both on the quantum state and the set of observables. In order to be consistent with the Heisenberg or Schrodinger equation, the quantum microstate must evolve according to a simple stochastic process which allows local transitions between the microstates. Macroscopic configurations correspond to the ergodic components of the stochastic process. In this way, the usual rules of the Copenhagen interpretation, including the Born rule, and a classical world emerge. The formalism also provides a quantum underpinning of statistical mechanics in a way that sweeps away the conceptual problems of its classical counterpart.
The Copenhagen Interpretation Born Again
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