  Using the most recent proper-motion determination of the old,
Solar-metallicity, Galactic open cluster M 67, in orbital computations in a
non-axisymmetric model of the Milky Way, including a bar and 3D spiral arms, we
explore the possibility that the Sun once belonged to this cluster. We have
performed Monte Carlo numerical simulations to generate the present-day orbital
conditions of the Sun and M 67, and all the parameters in the Galactic model.
We compute 3.5 \times 10^5 pairs of orbits Sun-M 67 looking for close
encounters in the past with a minimum distance approach within the tidal radius
of M 67. In these encounters we find that the relative velocity between the Sun
and M 67 is larger than 20 km/s. If the Sun had been ejected from M 67 with
this high velocity by means of a three-body encounter, this interaction would
destroy an initial circumstellar disk around the Sun, or disperse its already
formed planets. We also find a very low probability, much less than 10^-7, that
the Sun was ejected from M 67 by an encounter of this cluster with a giant
molecular cloud. This study also excludes the possibility that the Sun and M 67
were born in the same molecular cloud. Our dynamical results convincingly
demonstrate that M67 could not have been the birth cluster of our Solar System.
