Dingle's Paradoxes

The question of the relative velocity term is interesting. It points to another mistake. The usual idea is that v is the same for both obsrevers. But this is misleading. The observers in the two different frames use different standards of measure or different time and distance scales. But these are both magnified by the same dilation factor so when velocity is calculated in the two different frames the result is v in bot cases but the units of v are different because the time and distance scales are different. Einstein seems to have assumed that v was actually the same for observers in both frames and his failure to clarify this point is another source of confusion.

You are all talking models whereas the GPS is data that is corrected in a way that works OK for most cases but is not right. The clocks are both running at the same rate. No models data.