This paper is devoted to the study of stationary trajectories of free particles. From a classical point of view, this appears to be an almost trivial problem: Free particles should follow straight lines as predicted by Newton’s first law, and straight lines are indeed the stationary trajectories of the standard action integrals in the classical theory. In the following, however, a general relativistic approach is studied, and in this situation it is much less evident what action integral should be used. As it turns out, using the traditional Einstein–Hilbert principle gives us stationary states very much in line with the classical theory. But it is suggested that a different action principle, and in fact one which is closer to quantum mechanics, gives stationary states with a much richer structure: Even if these states in a sense can represent particles which obey the first law, they are also inherently rotating. Although we may still be far from understanding how general relativity and quantum mechanics should be united, this may give an interesting clue to why rotation (or rather spin, which is a different but related concept) seems to be the natural state of motion for elementary particles.