I just realized that the standard "twin paradox" in SR is actually a purely kinetic effect. It is solve by the obvious assymetry of the twins and the time dilation. However, the acceleration is not really needed in solving the paradox, since a third person could carry the clock backward after synchronization with the traveling twin. This shows it is only time dilation, a kinematic effect, that is at play there. However, if one consider a returning twin, then this twin will also experience an acceleration. Because of the equivalence principle, I guess that this will cause an additional time difference which is not caused by the pure time dilation of SR. It would be the result of the acceleration instead, just like a gravitational field will do. As I cannot develop that idea further, I would like your suggestions. Maybe I am wrong and doing double accounting? Also, I thought I could make a quick estimate using a equivalent potential for the acceleration. But on a second thought this looks strange to me, and I even question my understanding about why the potential appears in the gravity time dilation. Thanks for you ideas.