  A non-uniqueness result for the canonical structure in quantum theory shows
that the classical part of the Copenhagen interpretation contains physically
important information not contained in its quantum part. As a consequence, we
cannot compute the symmetry group of a quantum theory considering only the
quantum part. The unavoidable vagueness of the classical part therefore leads
to a similar vagueness in the definition of the symmetry group. This makes it
at least problematic, if not impossible, to establish the true symmetry group
of a quantum theory in the Copenhagen interpretation. Different from the old
measurement problem, the symmetry group is to important physically to be
rejected as a metaphysical pseudoproblem.
