# Complementarity has empirically relevant consequences for the definition of quantum states

## TL;DR

This paper argues that applying Bohr's complementarity to subsystems necessitates redefining quantum states as equivalence classes, aligning theory with experimental entropy and resolving conflicts in measurement theory.

## Contribution

It introduces a new definition of quantum states as equivalence classes, based on complementarity, which impacts the understanding of measurement in quantum mechanics.

## Key findings

- Redefining quantum states resolves measurement conflicts.
- Equivalence classes maximize information entropy.
- Current measurement theories conflict with experimental results.

## Abstract

The Copenhagen interpretation of quantum mechanics, which first took shape in Bohr's landmark 1928 paper on complementarity, remains an enigma. Although many physicists are skeptical about the necessity of Bohr's philosophical conclusions, his pragmatic message about the importance of the whole experimental arrangement is widely accepted. It is, however, generally also agreed that the Copenhagen interpretation has no direct consequences for the mathematical structure of quantum mechanics. Here I show that the application of Bohr's main concepts of complementarity to the subsystems of a closed system requires a change in the definition of the quantum state. The appropriate definition is as an equivalence class similar to that used by von Neumann to describe macroscopic subsystems. He showed that such equivalence classes are necessary in order to maximize information entropy and achieve agreement with experimental entropy. However, the significance of these results for the quantum theory of measurement has been overlooked. Current formulations of measurement theory are therefore manifestly in conflict with experiment. This conflict is resolved by the definition of the quantum state proposed here.