Relativistic Polygonal and Circular Paths: Solution for the Twins' Paradox Reviewed and Extended

Abstract

This article follows a previous one, which addressed the famous problem of Twins' Paradox: if one of two twins remains on Earth while the other gets on a rocket, travels at a speed close to the speed of light and returns, the traveler should find his brother older than himself. This is because, according to Special Relativity (SR), a moving clock runs slower than a 'stationary' one. The paradox lies in the fact that movement is relative, thus breaking the equivalence between frames of coordinates, a crucial principle at the heart of SR theory. The cited article highlighted the error in the premises that leads to the paradox, reanalyzing it and proving its non-existence either for a one-way or a round trip, despite the phenomenon of time dilation. An important extension of this conclusion is provided here. If one of the twins leaves the other, following a closed polygonal or circular path, in the end they find themselves at the same age. Thus, once again, the fundamental equivalency between frames of coordinates is fully respected. This – as before – is achieved by means of a new dilation factor, progressively