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.
Highlights
In classical physics, symmetry, reference frames and the relativity of physical quantities are intimately connected
In the quantum case, there arises an ambiguity regarding the definition of a reference frame: if it is classical, this raises the spectre of the lack of universality of quantum mechanics along with technical difficulties surrounding hybrid classicalquantum systems; if quantum, such a frame is subject to difficulties of definition and interpretation arising from indeterminacy, incompatibility, entanglement, and other quantum properties
The apparatus is not required to function as a reference system, which is internal to the measurement device and whose localisation controls the quality of the approximation by the absolute quantity
Summary
Symmetry, reference frames and the relativity of physical quantities are intimately connected.
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