Why Pure Quantum Theory Is Not Enough

The theory of KdV equations allows to construct examples of physically different canonical structures for the same Hamilton operator. These examples are unproblematic in pilot wave and dynamical collapse theories, which define a physically distinguished configuration space Q, and in the Copenhagen interpretation, which identifies the canonical operators with classical descriptions of the corresponding measurements. However, they become problematic in interpretations of quantum theory which reject the classical part of the Copenhagen interpretation, but do not add an appropriate replacement to it’s quantum part. We argue that such interpretations are not viable and have to be modified by introducing some additional structure. The ideal of a “pure interpretation” of quantum theory, which does not add anything to the quantum part, but allows to derive the classical part, has to be given up.