Symmetry, Reference Frames, and Relational Quantities in Quantum Mechanics

2017/03/30 by Leon Loveridge, Takayuki Miyadera, Paul Busch · 73 citations
Computer Science · Physics and Astronomy · #Formalism (music) #Observable #Quantum #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum Mechanics and Non-Hermitian Physics #Quantum process #Quantum state #Quantum system #Reference frame #Superselection #quant-ph

paper · pdf · doi:10.1007/s10701-018-0138-3

published in Foundations of Physics 48(2), 135-198 (Springer Science+Business Media) · Comments welcome

arxiv created 2017/03/30 · openalex created_date 2017/05/05 · openalex publication_date 2018/02/01 · arxiv updated 2018/03/14 · openalex updated_date 2026/08/05

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.

Citations

• Relational quantum mechanics

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