Alberto, it seems that you still haven't noticed that we've mostly been talking about the other part of the twin paradox. We weren't wondering about the fact THAT the twins have different ages - I believe that this is true has been established early. The fact is merely that people say (**NOT ME**, by the way. I add this disclaimer since that went wrong last time :P) that since everything is relative, you should be able to do the same for Twin B, giving you the opposite age difference. That this is false (because of the fact that twin B is not moving in an inertial frame, see below) has been established on page three.


However, I'm getting really tired of discussing this here, since - again - there is absolutely nothing LEFT to discuss.
I really feel that I've answered this "paradox" about ten times already. I really don't feel like doing it yet again.


But fine, one last time: Here's my answer regarding everything of the twin paradox: Calculate it in Twin A's system, which is an inertial frame. You'll get the result that we've seen above several times.
Now, since that it a completely tensorial equation, it'll be true in all coordinate systems.

Yes, different paths trough spacetime will have a different "length" (referring to the Minkowski-metric here, which, as we know, is no real metric), so the age-difference will depend on parameters that define the path, including the relative percentage of constant movement, acceleration and "turning around".



[The term "inertial frame" has definately something to do with the twin paradox: the formulas are only valid in inertial frames. Twin B's system is *NOT* an inertial frame. It follows that the equations cannot be used in his system - and applying them in that system was the essence of the twin paradox (well, it's second part)].