  Could the velocity spread, increasing with time, in the Galactic disk be
explained as a result of gravitational interactions of stars with giant
molecular clouds (GMCs) and spiral arms? Do the old open clusters high above
the Galactic plane provide clues to this question? We explore the effects on
stellar orbits of scattering by inhomogeneities in the Galactic potential due
to GMCs, spiral arms and the Galactic bar, and whether high-altitude clusters
could have formed in orbits closer to the Galactic plane and later been
scattered.
  Simulations of test-particle motions are performed in a realistic Galactic
potential. The effects of the internal structure of GMCs are explored. The
destruction of clusters in GMC collisions is treated in detail with N-body
simulations of the clusters.
  The observed velocity dispersions of stars as a function of time are well
reproduced. The GMC structure is found to be significant, but adequate models
produce considerable scattering effects. The fraction of simulated massive old
open clusters, scattered into orbits with |z| > 400 pc, is typically 0:5%, in
agreement with the observed number of high-altitude clusters and consistent
with the present formation rate of massive open clusters.
  The heating of the thin Galactic disk is well explained by gravitational
scattering by GMCs and spiral arms, if the local correlation between the GMC
mass and the corresponding voids in the gas is not very strong. Our results
suggest that the high-altitude metal-rich clusters were formed in orbits close
to the Galactic plane and later scattered to higher orbits. It is possible,
though not very probable, that the Sun formed in such a cluster before
scattering occurred.
