In the standard twin "paradox" scenario, with an instantaneous turnaround (which requires an infinite acceleration by the traveling twin that lasts only an infinitesimal time), what makes it SEEM paradoxical is that the traveling twin ("he") is inertial during what SEEMS like essentially his entire trip ... inertial all except the single instant of the turnaround. And SURELY the home twin ("she") couldn't possibly age any during that single instant in the traveling twin's life, COULD she? While the traveling twin is inertial, he in entitled to use the famous time dilation result, which tells him that the home twin is ageing more slowly than he is. So it SEEMS paradoxical that, when the twins are reunited, he finds that it is the home twin who is the older. The resolution of the "paradox" is that, according to the traveling twin, the home twin ages by a very large amount during that one instant in his life at his turnaround. The implicit assumption that nothing could happen to the home twin's age during that single instant in the traveling twin's life at the turnaround was wrong. It is often claimed that acceleration by the traveling twin cannot be the resolution of the twin "paradox" because an equivalent scenario, one with no acceleration, can also resolve the "paradox". The revised scenario says that a third person (perpetually inertial) could just happen to be passing by (and momentarily co-located with) the traveling twin at the point where the traveler intended to do his instantaneous turnaround. (This third person has always been, and will continue to be, headed toward the home twin.) And it just coincidentally happens that that third person has exactly the same age as the traveling twin when they are momentarily co-located. So the traveling twin decides not to accelerate (and just continue moving away from the home twin), and it is just the third person who meets up later with the home twin. At the meet-up, the third person will be exactly as old as the traveling twin would have been at his reunion with the home twin, if he had instantaneously turned around as originally planned. So it is then contended that this scenario is completely equivalent to the original scenario, but without any acceleration. But that contention is not correct. If the third person is really to be a VALID substitute for the traveling twin at the instant of his meet-up with the home twin, in the sense of fully addressing the original "paradox", the third person's total ageing, ACCORDING TO THE TRAVELING TWIN, during the ENTIRE trip (beginning with the separation of the two twins) MUST be the same as the total ageing that the traveling twin WOULD have experienced if the traveling twin had turned around as originally planned. And since the third person (by design) has the same age when he meets up with the home twin as the traveling twin would have had at the reunion (if he had done the turnaround as originally planned), it follows that the third person (if he is to be a valid substitute for the traveling twin) HAD to be age zero, according to the traveling twin, when the traveling twin started his trip. But that is not the case, which can be seen from the following numerical example. Let the gamma factor for the two twins' relative motion be equal to 2, which implies that their relative velocity (traveling away from other) is v = 0.8660... ly/y . Let the traveling twin be 10 years old at the (originally planned) turnaround point. According to the home twin, the third person is traveling at the same speed toward her. To determine the speed W at which the traveling twin and the third person are approaching each other (according to each other), we must use the relativistic addition of velocities result: W = 2v / (1 + v * v) = 0.98974... ly/y , which gives a gamma factor of GAMMA = 7. (I use capital letters for this gamma factor, to distinguish it from the gamma factor of the relative motion between the two twins.) So what does the traveling twin say is the age of the third party at the beginning of the scenario (right when the traveling twin starts moving away from the home twin)? He says that the third person is ageing 7 times slower that he is, so while the traveling twin was ageing by 10 years getting to the turn point, the third person was ageing by 10/7 = 1.4285... years. So the third person was 10 - 1.4285 = 8.5714 years old at the beginning of the scenario. Since he was NOT zero years old then, he CANNOT (in the opinion of the traveling twin) be a valid substitute for the traveling twin for the purpose of resolving the twin "paradox". So the two scenarios are NOT equivalent, and the non-acceleration argument is a red herring ... it does not resolve the paradox.