Hi I´ve got some question about this paradox (and the whole relativity theory) too but first of all I want to apologize for my poor english. If there's one thing I've understood (reading here and there on the web) it is that it is impossible to determine who is at rest and who is in motion. An observer can perceive only the accelerations (or decelerations) but also in this case he cannot know if he passed from a rest condition to motion or vice versa, or if he simply changed speed within a motion condition. The whole universe is at the same time moving at constant speed and at rest (unless it is accelerating). We see a cosmic ray that travels almost at the speed of light but for the cosmic ray we are traveling almost at the speed of light. Could you please confirm this first part? Now comes the question about the twin paradox, since I still have not figured out if you get old slower when traveling fast (compared to what has to be clarified) or when accelerating or both, I want to propose a modified version: Imagine an "empty" universe, no important masses and only two observers each with its own clock. These two observers move towards one another with relative speed next to the speed of light. Obviously it makes no sense to say that one is in motion and one is stationary but for simplicity we imagine that the observer A is "stationary" and sees B approach at nearly the speed of light. The moment they cross they synchronize the clocks. At this point A will see B receding. Now imagine for simplicity of depiction that the universe in which the observers are located do not have 3 spatial dimensions but only 2. In particular we imagine that this two-dimensional universe (three-dimensional with time) is the surface of a sphere. Consequently B continuing on his way sooner or later will meet with A again after traveling a "full circle" of the spherical universe. My question is what will the observers see when they will compare the clocks? there was no acceleration. According to each observer they were stationary and saw the other going away (or getting closer) at the speed of light. Who will be older than the other? I hope that people will be able to clarify these doubts.