What can we do in a symmetry-constrained perspective? The importance of the total charge's status in quantum reference frame frameworks

Abstract

The study of quantum reference frames has received renewed interest over the last years, leading to the parallel development of non-equivalent frameworks by different communities. We clarify the differences between these frameworks. At the mathematical level, they mainly differ in the kind of symmetry (either weak or strong) employed to constrain the system. We show that this mathematical difference corresponds to a fundamental physical question: whether the global charge associated to the symmetry group is accessible to symmetry-constrained observers. In this context, we formulate a definition of a perspective in terms of operational capacities, or lack thereof. Turning to consequences of adopting either approach, we discuss how adopting the weak approach induces an ambiguity in the momenta included in each perspective and bars from defining reversible QRF transformations. We then review and analyze the existing arguments motivating each approach, and show how they bear upon the problem of charge accessibility. Finally, we introduce a simple operational scenario in which upholding two reasonable physical postulates leads to the conclusion that internal observers could measure the global charge by 1/ performing a relativized interference measurement and 2/ classically communicating.

25+6 pages. Comments are welcome!

References in corpus (28)

• Reference frames, superselection rules, and quantum information
• The resource theory of quantum reference frames: manipulations and monotones
• Measuring the quality of a quantum reference frame: the relative entropy of frameness
• An effective approach to the problem of time
• Effective approach to the problem of time: general features and examples
• Quantum Gravity and Higher Curvature Actions
• Quantum reference frames for general symmetry groups
• Effective Constraints for Quantum Systems
• Spacetime Quantum Reference Frames and superpositions of proper times
• Edge modes as reference frames and boundary actions from post-selection
• Quantum reference frame transformations as symmetries and the paradox of the third particle
• Edge modes as dynamical frames: charges from post-selection in generally covariant theories
• The group structure of dynamical transformations between quantum reference frames
• Internal quantum reference frames for finite Abelian groups
• Causal structure in the presence of sectorial constraints, with application to the quantum switch
• Quantum Reference Frames at the Boundary of Spacetime
• Operational Quantum Reference Frame Transformations
• Identification is Pointless: Quantum Coordinates, Localisation of Events, and the Quantum Hole Argument
• Communicating without shared reference frames
• Embedding cyclic information-theoretic structures in acyclic spacetimes: no-go results for indefinite causality
• On the Meaning of Local Symmetries: Epistemic-Ontological Dialectics
• Soft edges: the many links between soft and edge modes
• Quantum conformal symmetries for spacetimes in superposition
• Semiclassical States on Lie Algebras
• Indefinite causal order and quantum coordinates
• An algebraic approach to the "frozen formalism" problem of time
• Algebraic properties of quantum reference frames: Does time fluctuate?
• Searching for a physical description relative to a quantum system