  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 "totalitarian 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.
