The traveling twins paradox and special relativity

A modified version of the twin paradox (TP) thought experiment, termed the traveling TP (TTP), is described. In the TTP, the twins move toward each other, via two identical fast vehicles, from two starting points, located along the x axis at coordinates +(l+ Δl) and ‐(l+ Δl), respectively. The twins first accelerate up to velocity v along identical runways of length Δl each, then they shut down engines and travel toward each other with constant equal velocities (v). After passing each other, they use the same runways to decelerate and stop. The scenario of the TTP is completely symmetric, implying that it is impossible to prefer one reference frame over the other, as done in special relativity's solution of the TP. Moreover, in the range (−l, +l) the TTP system is an inertial one. The complete symmetry of TTP should lead to a symmetric solution, according to which the twins should pass each other at x = 0 to find that they have aged equally. However, applying special relativity to the TTP results in a contradiction, according to which each twin will measure a time dilation relative to the other twin.