In this and the following chapter I apply the present interpretation of quantum mechanics to coupled systems of the type studied by Einstein et al. (1935), Bohm (1951), Bell (1964), and Aspect et al. (1982a, 1982b) (to name just a few seminal contributors to the large and growing literature on this topic). The main conclusions were already anticipated in Chapter 1. In the present interpretation, quantum mechanics offers a detailed theoretical account of the physical events and processes that underlie the correlations exhibited in measurements on such systems. This account depends both on the postulation of irreducible properties of compound systems, and also on the treatment of measurement as a quantum mechanical interaction. In the present chapter I present technical details of this account, and in the next chapter I explore its metaphysical aspects and implications, especially for the notions of holism and causal explanation.

For concreteness, I restrict attention here to systems composed of two spin-½ atomic systems: The generalization to other pairs of systems with different spins is straightforward. Such systems may result from a prior interaction between the two component systems, or they may be produced de novo (as a positron-electron pair may be produced by annihilation of a γ-ray). Call the component systems A, B and the compound system A⊕B. The system representative of A⊕B will be a subspace of the tensor product Hilbert space HA⊗HB.