Symmetry, Reference Frames, and Relational Quantities in Quantum Mechanics

Leon Loveridge, Takayuki Miyadera, Paul Busch

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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.
Original languageEnglish
Number of pages64
JournalFoundations of Physics
Publication statusPublished - 5 Feb 2018

Bibliographical note

© The Author(s) 2018.


  • quantum measurement
  • symmetry
  • reference frame

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