The Quantum Totalitarian Property and Exact Symmetries [article]

Chiara Marletto, Vlatko Vedral
We discuss a point, which from time to time has been doubted in the literature: all symmetries, such as those induced by the energy and momentum conservation laws, hold in quantum physics not just "on average", as is sometimes claimed, but exactly in each "branch" of the wavefunction, expressed in the basis where the conserved observable is sharp. We note that for conservation laws to hold exactly for quantum systems in this sense (not just on average), it is necessary to assume the so-called
more » ... otalitarian property of quantum theory", namely that any system capable of measuring a quantum observable must itself be quantised. Hence, if conservation laws are to hold exactly, the idea of a 'classical measuring apparatus' (i.e., not subject to the branching structure) is untenable. We also point out that any other principle having a well-defined formulation within classical physics, such as the Equivalence principle, is also to be extended to the quantum domain in exactly the same way, i.e., branch by branch.
doi:10.48550/arxiv.2005.00138 fatcat:cxsxkdhlt5gavls7hlvbyqe24a