Interaction between classical and quantum systems: a new approach to quantum measurement. I

We introduce an unconventional approach to the measurement problem in quantum mechanics: we treat the apparatus as a classical system belonging to the macroworld. To describe the quantum measurement process we must couple the classical apparatus to the quantum system. In this paper we explain how this is to be done: we embed the classical apparatus into a larger quantum-mechanical structure, making use of a superselection principle. The apparatus can now be coupled to the quantum system in a straightforward manner. We discuss what constraints should be placed on the coupling so that an interpretation of the interaction as a measurement results. We require that unambiguous information of the values of a quantum observable should be transferred to the variables of the apparatus. We also require that the apparatus should retain its classical identity. This latter requirement is formulated as a principle of integrity, in both weak and strong forms