Symmetry, Reference Frames, and Relational Quantities in Quantum Mechanics

TY - JOUR

T1 - Symmetry, Reference Frames, and Relational Quantities in Quantum Mechanics

AU - Loveridge, Leon

AU - Miyadera, Takayuki

AU - Busch, Paul

N1 - © The Author(s) 2018.

PY - 2018/2/5

Y1 - 2018/2/5

N2 - 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.

AB - 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.

KW - QUANTUM THEORY

KW - quantum measurement

KW - symmetry

KW - reference frame

UR - https://arxiv.org/abs/1703.10434

U2 - 10.1007/s10701-018-0138-3

DO - 10.1007/s10701-018-0138-3

M3 - Article

SN - 0015-9018

JO - Foundations of Physics

JF - Foundations of Physics

ER -