I am trying to understand if SR can explain a real, measurable velocity time dilation as seen in experiments/observations like GPS satellite or Bailey et. al. Let us say we have twins sitting in their identical, individual spaceships in space, close to each other, and far away from any large masses. One of them fires his engine and goes some distance at high velocity, reverses, and comes back to the original location. Would he really have aged less than the stationary twin, and if so why? I have seen the explanations based on the traveling twin not being in an inertial frame at all times, but do not find them conclusive. I mean, from SR perspective, when the traveling twin is accelerating, he may consider from his point of view that the stationary twin is in a non-inertial frame, while he is in an inertial one. Since there is no third party observer involved, each twin should be entitled to expect that the other has aged less by a specific amount (as per SR formula). I am thinking that the traveling twin feeling acceleration should not differentiate between the twins from an SR perspective, since we cannot consider the acceleration asymmetrically (i.e. both twins are identically accelerating or in uniform motion w.r.t. each other at all times, from SR perspective). So, how would SR predict correctly whose clock will turn out to have recorded a longer passage of time if this is a real experiment?