Symmetry, Reference Frames, and Relational Quantities in Quantum Mechanics

Abstract

We propose that observables in quantum theory are properly understood as representatives of symmetry-invariant quantities relating one system to another, the latter to be called a reference system. We provide a rigorous mathematical language to introduce and study quantum reference systems, showing that the orthodox "absolute" quantities are good representatives of observable relative quantities if the reference state is suitably localised. We use this relational formalism to critique the literature on the relationship between reference frames and superselection rules, settling a long-standing debate on the subject.

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Cited by in corpus (50)

• Quantum mechanics and the covariance of physical laws in quantum reference frames
• The Trinity of Relational Quantum Dynamics
• Quantum clocks observe classical and quantum time dilation
• Quantum superposition of spacetimes obeys Einstein's Equivalence Principle
• Equivalence of approaches to relational quantum dynamics in relativistic settings
• Quantum reference frames for general symmetry groups
• Spacetime Quantum Reference Frames and superpositions of proper times
• Quantum Relativity of Subsystems
• Quantum reference frame transformations as symmetries and the paradox of the third particle
• Quantum reference frames, measurement schemes and the type of local algebras in quantum field theory
• The group structure of dynamical transformations between quantum reference frames
• Internal quantum reference frames for finite Abelian groups
• Relational observables, reference frames, and conditional probabilities
• Second-quantized Unruh-DeWitt detectors and their quantum reference frame transformations
• Relative Quantum Time
• Understanding quantum mechanics: a review and synthesis in precise language
• Switching Quantum Reference Frames for Quantum Measurement
• Quantum Reference Frames at the Boundary of Spacetime
• Transformation of Spin in Quantum Reference Frames
• Quantum reference frames for an indefinite metric
• Operational Quantum Reference Frame Transformations
• Time Observables in a Timeless Universe
• Identification is Pointless: Quantum Coordinates, Localisation of Events, and the Quantum Hole Argument
• Quantifying quantum reference frames in composed systems: local, global and mutual asymmetries
• Entanglement-asymmetry correspondence for internal quantum reference frames
• A relational perspective on the Wigner-Araki-Yanase theorem
• Inference of gravitational field superposition from quantum measurements
• A model of quantum spacetime
• Gravitational entropy is observer-dependent
• Measurement disturbance and conservation laws in quantum mechanics
• Indefinite causal order and quantum coordinates
• Crossed products and quantum reference frames: on the observer-dependence of gravitational entropy
• Generalised second law beyond the semiclassical regime
• Blurred quantum Darwinism across quantum reference frames
• The sum of entanglement and subsystem coherence is invariant under quantum reference frame transformations
• Quantum Origin of (Newtonian) Mass and Galilean Relativity Symmetry
• Self-consistency of the two-point energy measurement protocol
• Classicality of the heat produced by quantum measurements
• Infinitesimal reference frames suffice to determine the asymmetry properties of a quantum system
• A quantum reference frame size-accuracy trade-off for quantum channels
• Uncertainty Relations Relative to Phase-Space Quantum Reference Frames
• Quantum Mechanics from Relational Properties, Part III: Path Integral Implementation
• Quantum Gravity, Hydrodynamics and Emergent Cosmology: A Collection of Perspectives
• What can we do in a symmetry-constrained perspective? The importance of the total charge's status in quantum reference frame frameworks
• Quantum Galilei group as quantum reference frame transformations
• Towards a Quantum Erlangen Program
• Quantum Mechanics Relative to a Quantum Reference System: a Relative State Approach
• Can we accurately read or write quantum data?
• Relational space-time and de Broglie waves
• Quantum reference frames for spacetime symmetries and large gauge transformations