I accept that, for that is what I originally understood, but I was recently told you can't tell who is moving with respect to whom, so it is a lottery as to who will be the youngest when they get back together, for I was told they each think the other is moving and staying younger than the observer. But the ultimate proof is when they do return, the younger was in the non-inertial frame.
So how do you think and can rapidly tell which is the inertial and the non inertial frame at the start or during the experiment? OK it is possible to tell at the end but how do you know earlier than that?
The non-inertial observer is the one that changes his velocity in order to return to the other observer. The inertial observer never changes his velocity, he always remains in the same inertial frame. The non-inertial observer changes inertial frames. He is in one inertial frame while they are separating, then changes to another inertial frame so that they will come back together. This switch of inertial frame also causes a change in what time he thinks it is back at the inertial observer's position. It will go from being behind his to being ahead of his.
I'm going to use an analogy to explain what I mean.
Imagine two men walking side by side at the same pace on a featureless plane. One of the men(man1) turns and walks in a different direction without changing his pace. After a while he looks to see how the other man (man 2) is progressing. He will note that man 2 is behind him, and that man 2 has made less progress in the direction that he himself is walking. Man 2 makes the same observation, that he has made more progress in the direction that
he is walking than man 1 is. Since each man judges progress as distance traveled in the direction that he himself is walking, he sees the other man as falling behind.
This is the equivalent of time dilation, where clocks in motion with respect to each other see each other as running slow. The direction each man is walking is the equivalent of his inertial frame.
Note that the distinction of which man is
really making less progress entirely depends on which direction the observer himself happens to be facing and that there is no one "true" direction from which we can make this determination.
Now Let's say that man 1 turns again, this time back so that he will intersect man 2's path (man 2 continues as normal). What does he see happening to man 2? He will appear to go from being behind man 1 to being in front of him. man 1 has changed to a new inertial frame, and in this one Man 2 is ahead of him. Since he still judges progress according to the direction he is facing, man 2 suddenly has made more progress than he has!
Man 2 only notices that man 1 has changed direction, but man 1 still remains behind him.
Man 1 continues until he intersects man 2's path and then turns a third time so that he faces the same direction as man 2. He will find that he is behind man 2.( a fact that man 2 concurs with). This is the equivalent of the traveling observer returning to find that he has aged less.
The fact that man 1 ends up behind man 2 has to do with the fact that after their paths had diverged, he changed direction. If, on the other hand, man 2 had changed direction,
he would have been the one who found himself behind when they crossed each others path again. (note that it doesn't matter which one of them initially changes direction to start the divergence, only which one turned to return them to the same path.
So the upshot is that while both men agree as to the final outcome, they will disagree as to how this outcome came about. This is the thing about Relativity; everyone will agree as to what two clocks read when then meet, they just might not agree as to how things got that way.
