  Among several possibilities for what reality could be like in view of the
empirical facts of quantum mechanics, one is provided by theories of
spontaneous wave function collapse, the best known of which is the
Ghirardi-Rimini-Weber (GRW) theory. We show mathematically that in GRW theory
(and similar theories) there are limitations to knowledge, that is, inhabitants
of a GRW universe cannot find out all the facts true about their universe. As a
specific example, they cannot accurately measure the number of collapses that a
given physical system undergoes during a given time interval; in fact, they
cannot reliably measure whether one or zero collapses occur. Put differently,
in a GRW universe certain meaningful, factual questions are empirically
undecidable. We discuss several types of limitations to knowledge and compare
them with those in other (no-collapse) versions of quantum mechanics, such as
Bohmian mechanics. Most of our results also apply to observer-induced collapses
as in orthodox quantum mechanics (as opposed to the spontaneous collapses of
GRW theory).
