Well, it can be said that, disregarding all frames of reference, that for the two objects relative to each other, one of them will experience time dilation (the one traveling faster) and the other will not.
What if you treat the traveler as one entity, and the rest of the universe as the other entity. For whom will the time be slowed down for? Is the traveler traveling at near speed of light relative to the universe, thus slowing his own time down compared to the rest of the universe? Or is the rest of the universe traveling at the near speed of light, thus leaving the traveler the only one experiencing the "actual" sense of time?