  Quantum states containing records of incompatible outcomes of quantum
measurements are valid states in the tensor-product Hilbert space. Since they
contain false records, they conflict with the Born rule and with our
observations. I show that excluding them requires a fine-tuning to an extremely
restricted subspace of the Hilbert space that seems "conspiratorial", in the
sense that (1) it seems to depend on future events that involve records
(including measurement settings) and on the dynamical law (normally thought to
be independent of the initial conditions), and (2) it violates Statistical
Independence, even when it is valid in the context of Bell's theorem. To solve
the puzzle, I build a model in which, by changing the dynamical law, the same
initial conditions can lead to different histories in which the validity of
records is relative to the new dynamical law. This relative validity of the
records may restore causality, but the initial conditions still must depend, at
least partially, on the dynamical law. While violations of Statistical
Independence are often seen as non-scientific, they turn out to be needed to
ensure the validity of records and our own memories and, by this, of science
itself. A Past Hypothesis is needed to ensure the existence of records and
turns out to require violations of Statistical Independence. It is not excluded
that its explanation, still unknown, ensures such violations in the way needed
by local interpretations of quantum mechanics. I suggest that an as-yet unknown
law or superselection rule may restrict the full tensor-product Hilbert space
to the very special subspace required by the validity of records and the Past
Hypothesis.
