When you say "massive particle", is that any particle with mass?
Do the different paths through Reimannian space correspond to different paths in Euclidean space? In other words, we can observe massive and massless particles following these different paths?
Thanks for the info, one more question. CD's answer about needing "some decent source of curvature" hints that we don't yet have experimental or observational confirmation of massive and massless particles following different paths - is that true?