A symmetry problem in the Copenhagen interpretation

TL;DR

This paper demonstrates that the classical component of the Copenhagen interpretation introduces non-uniqueness in symmetry groups, complicating the understanding of quantum symmetries due to classical vagueness.

Contribution

It reveals the non-uniqueness of the canonical structure in quantum theory and its implications for symmetry group determination within the Copenhagen interpretation.

Findings

Classical part contains essential information not in the quantum part.

Symmetry group cannot be fully determined from the quantum part alone.

Vagueness in classical part affects the definition of quantum symmetries.

Abstract

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.