Kabel, Viktoria and de la Hamette, Anne-Catherine and Apadula, Luca and Cepollaro, Carlo and Gomes, Henrique and Butterfield, Jeremy and Brukner, Caslav
(2024)
Identification is Pointless: Quantum Reference Frames, Localisation of Events,
and the Quantum Hole Argument.
[Preprint]
Abstract
The study of quantum reference frames (QRFs) is motivated by the idea of taking into account the quantum properties of the reference frames that we use, explicitly or implicitly, in our description of physical systems. Like a classical reference frame, a QRF can be used to define physical quantities such as time, position, momentum, and spin relationally. Unlike its classical analogue, it relativises the notions of superposition and entanglement of quantum systems. Here, we provide a novel explanation for the frame-dependence of superposition and entanglement by tracing it back to the question of 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. Thus, sameness and difference — and, as a result, 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 the spacetime points in the different branches. This allows us to determine whether a given event is located at “the same” or “different” points in the superposed spacetimes. Because this feature depends on the choice of QRF, we argue that the localisation of an event should not be seen as an inherent property of the event. This alleviates previously voiced concerns that QRF changes could have empirical consequences for interference experiments, such as the Bose et al.-Marletto-Vedral proposal. Moreover, it implies that the number of events is equal in both the flat and the curved spacetime implementations of quantum-controlled causal order. We conclude with the “quantum hole argument” as a generalisation for the quantum context of Einstein’s famous hole argument, arguing that not just spacetime points but also their identification and the localisation of events across manifolds in superposition lose their absolute physical meaning in the presence of quantum symmetries.
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