  The meaning of superselection rules in Bohm-Bell theories (i.e., quantum
theories with particle trajectories) is different from that in orthodox quantum
theory. More precisely, there are two concepts of superselection rule, a weak
and a strong one. Weak superselection rules exist both in orthodox quantum
theory and in Bohm-Bell theories and represent the conventional understanding
of superselection rules. We introduce the concept of strong superselection
rule, which does not exist in orthodox quantum theory. It relies on the clear
ontology of Bohm-Bell theories and is a sharper and, in the Bohm-Bell context,
more fundamental notion. A strong superselection rule for the observable G
asserts that one can replace every state vector by a suitable statistical
mixture of eigenvectors of G without changing the particle trajectories or
their probabilities. A weak superselection rule asserts that every state vector
is empirically indistinguishable from a suitable statistical mixture of
eigenvectors of G. We establish conditions on G for both kinds of
superselection. For comparison, we also consider both kinds of superselection
in theories of spontaneous wave function collapse.
