Relativity of Quantum States and Observables

TL;DR

This paper investigates how quantum states and observables relate under symmetry transformations, proposing a relativisation approach that offers new insights into quantum superpositions and coherence.

Contribution

It introduces a relativisation mapping as a quantum reference frame, clarifying when standard quantum descriptions approximate relative ones.

Findings

Standard quantum descriptions approximate relative ones with localisable reference systems.

Provides a new perspective on the reality of quantum superpositions.

Connects symmetry invariance with measurement statistics in quantum mechanics.

Abstract

Under the principle that quantum mechanical observables are invariant under relevant symmetry transformations, we explore how the usual, non-invariant quantities may capture measurement statistics. Using a relativisation mapping, viewed as the incorporation of a quantum reference frame, we show that the usual quantum description approximates the relative one precisely when the reference system admits an appropriate localisable quantity and a localised state. From this follows a new perspective on the nature and reality of quantum superpositions and optical coherence.