  We investigate the long-term evolution of the inclinations of the known
classical and resonant Kuiper belt objects (KBOs). This is partially motivated
by the observed bimodal inclination distribution and by the putative physical
differences between the low- and high-inclination populations. We find that
some classical KBOs undergo large changes in inclination over gigayear
timescales, which means that a current member of the low-inclination population
may have been in the high-inclination population in the past, and vice versa.
The dynamical mechanisms responsible for the time-variability of inclinations
are predominantly distant encounters with Neptune and chaotic diffusion near
the boundaries of mean motion resonances. We reassess the correlations between
inclination and physical properties including inclination time-variability. We
find that the size-inclination and color-inclination correlations are less
statistically significant than previously reported (mostly due to the increased
size of the data set since previous works with some contribution from
inclination variability). The time-variability of inclinations does not change
the previous finding that binary classical KBOs have lower inclinations than
non-binary objects. Our study of resonant objects in the classical Kuiper belt
region includes objects in the 3:2, 7:4, 2:1, and eight higher-order mean
motion resonances. We find that these objects (some of which were previously
classified as non-resonant) undergo larger changes in inclination compared to
the non-resonant population, indicating that their current inclinations are not
generally representative of their original inclinations. They are also less
stable on gigayear timescales.
