# 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.

## Key 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.