A contextual Planck parameter and the classical limit in quantum
  cosmology
  We propose that whatever quantity controls the Heisenberg uncertainty
relations (for a given complementary pair of observables) it should be
identified with an effective Planck parameter. With this definition it is not
difficult to find examples where the Planck parameter depends on the region
under study, varies in time, and even depends on which pair of observables one
focuses on. In quantum cosmology the effective Planck parameter depends on the
size of the comoving region under study, and so depends on that chosen region
and on time. With this criterion, the classical limit is expected, not for
regions larger than the Planck length, $l_{P}$, but for those larger than
$l_{Q}=(l_{P}^{2}H^{-1})^{1/3}$, where $H$ is the Hubble parameter. In theories
where the cosmological constant is dynamical, it is possible for the latter to
remain quantum even in contexts where everything else is deemed classical.
These results are derived from standard quantization methods, but we also
include more speculative cases where ad hoc Planck parameters scale differently
with the length scale under observation. Even more speculatively, we examine
the possibility that similar complementary concepts affect thermodynamical
variables, such as the temperature and the entropy of a black hole.
