Identification is Pointless: Quantum Coordinates, Localisation of Events, and the Quantum Hole Argument

TL;DR

This paper explores how quantum reference frames affect the identification of configurations and events, revealing that notions of sameness, difference, and localization are frame-dependent in quantum superpositions.

Contribution

It introduces a framework for understanding how quantum reference frames relativize superposition, entanglement, and event localization, extending Einstein's hole argument to quantum settings.

Findings

Localization of events depends on the choice of quantum reference frame

Superposition and entanglement lose absolute meaning in quantum reference frames

Frame-dependence impacts the understanding of causal order and locality

Abstract

The study of quantum reference frames (QRFs) is motivated by the idea of taking into account the quantum properties of the reference frames used, explicitly or implicitly, in our description of physical systems. Like classical reference frames, QRFs can be used to define physical quantities relationally. Unlike their classical analogue, they relativise the notions of superposition and entanglement. Here, we explain this feature by examining how configurations or locations are identified across different branches in superposition. We show that, in the presence of symmetries, whether a system is in "the same" or "different" configurations across the branches depends on the choice of QRF. Hence, sameness and difference -- and thus superposition and entanglement -- lose their absolute meaning. We apply these ideas to the context of semi-classical spacetimes in superposition and use coincidences of four scalar fields to construct a comparison map between spacetime points in the different branches. This reveals that the localisation of an event is frame-dependent. We discuss the implications for indefinite causal order and the locality of interaction and conclude with a generalisation of Einstein's hole argument to the quantum context.