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Abstract

The so-called Twins’ Paradox has been a controversial issue for more than a century, concerning the foundations of modern physics, in this case, the credibility of special relativity itself. In fact, how can a supposed credible theory predict paradoxes, if one assumes that there can be no paradoxes in Nature? Since Einstein’s founding paper, the phenomenon of time dilation has been mistakenly used to construct a seemingly insoluble contradiction at the heart of the theory, calling into question the fundamental equivalence between inertial frames of coordinates. In an early paper on the subject, I proved that, whether on a one-way trip or a linear round trip, there is no paradox at all: twins meet again at the same age, and this despite time-dilation. Regarding the round trip, a new dilation factor emerged, in an equation for the final time that is precisely the same for the reference frame of each twin. In a second paper, by means of a well-founded conjecture, these conclusions were generalized to closed regular polygonal paths and, in the limit, to circular paths. A generalized equation was proposed and thoroughly verified, while various aspects of the problem were addressed and highlighted. However, it was only a conjecture, formal proof was missing. This paper brings that proof, thus turning the conjecture into a theorem, i.e., a scientific fact.