Identification is Pointless: Quantum Coordinates, Localisation of Events, and the Quantum Hole Argument (2402.10267v2)

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.

• The paper demonstrates that quantum superposition and entanglement are frame-dependent, altering standard event identification.
• It introduces a mapping method using scalar field coincidences to localize events in semi-classical spacetimes.
• The study generalizes Einstein's hole argument, showing that QRF shifts maintain a constant number of events.

Overview of "Identification is Pointless: Quantum Reference Frames, Localisation of Events, and the Quantum Hole Argument"

The paper "Identification is Pointless: Quantum Reference Frames, Localisation of Events, and the Quantum Hole Argument" presents an exploration of the theoretical foundations and implications of quantum reference frames (QRFs) in the context of quantum mechanics and general relativity. The authors, Kabel et al., from institutions such as the Austrian Academy of Sciences and Trinity College, University of Cambridge, explore the consequences of adopting QRFs, especially regarding the notions of superposition, entanglement, and the localization of events.

The paper is premised on the need to incorporate the quantum properties of reference frames used implicitly or explicitly when dealing with physical systems. Traditional frameworks use classical reference frames to define quantities like time, position, momentum, and spin. In quantum mechanics, however, these quantities are subject to relativization due to superposition and entanglement. The authors propose a novel explanation for the frame-dependence of these quantum properties, linking this dependency to the ability (or lack thereof) to identify configurations or locations across superposed branches of quantum states.

Key Arguments and Results

1. Frame-dependence of Superposition and Entanglement:
   • The paper illustrates that superposition and entanglement depend on the choice of QRF due to the inherent symmetries of quantum systems. The authors argue that whether a system is perceived as the same or different across branches in superposition changes with the QRF, thus eliminating absolute meanings for these properties.
2. Application to Semi-classical Spacetimes:
   • The authors extend the concept of QRFs to semi-classical spacetimes in superposition, where conventional notions of event localization are challenged. They propose using a comparison map between spacetime points across different branches, constructed through the coincidences of four scalar fields. This map enables assessment of whether events are localized at coinciding or disparate points across superposed spacetimes.
3. Influences on Quantum and Classical Symmetries:
   • A generalization to quantum systems of Einstein's hole argument is proposed, where not only spacetime points but also their identifications across different superposed manifolds lose their inherent physical meaning. The authors argue that QRF changes should not have empirical consequences for interference experiments and maintain that the number of events remains constant in both flat and curved spacetime implementations of quantum-controlled causal orders.

Theoretical Implications

The paper's implications are significant both practically and theoretically. Practically, understanding QRFs could refine experimental setups in quantum mechanics and quantum gravity, ensuring that assumptions about reference frames are sound. Theoretically, it expands the field of quantum mechanics by offering a robust framework that accommodates frame-dependence of quantum properties, prompting reconsideration of foundational notions like causal order and the essence of quantum events.

Future Developments

Going forward, the incorporation of QRFs in quantum gravity models holds promise for resolving ambiguities in the treatment of space and time at the quantum level. Further development could deeply influence theories of quantum cosmology and the paper of quantum information in curved spacetime. Moreover, experimental validation of the theoretical predictions concerning QRF-induced frame-dependence is a fertile ground for future research, potentially uncovering new quantum phenomena.

In conclusion, this paper provides a comprehensive investigation into the use of QRFs, offering a graceful extension of classical concepts into the quantum domain while challenging researchers to reevaluate their understanding of quantum systems' spacetime at a foundational level.