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.
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