I Why does time dilation only affect one of the twins?

[Freixas]

No. There is no standard method for forming a non inertial frame. That is part of the problem.

My preferred approach is radar coordinates. This avoids the overlaps and gaps of the naive approach, and it is the only convention I know thrust respects the second postulate.

Thanks, Dale.

Perhaps you can help clarify post #10 for me. It appears to me to propose a mapping and then lists some problems that the mapping reveals. Are the problems universal (missing worldlines and events, events appearing twice) or are these more a reflection of the choice of mapping?

While I would love to see your radar version of the twins paradox diagram I posted, I know that's asking a lot. I looked up radar coordinates, but it would be really helpful to see the diagram that I posted converted to your preferred approach by someone who actually knows what he is doing.

 

[Dale]

Are the problems universal (missing worldlines and events, events appearing twice) or are these more a reflection of the choice of mapping?

Those are a pathology of the "naive" approach to constructing a non-inertial frame.

While I would love to see your radar version of the twins paradox diagram I posted, I know that's asking a lot. I looked up radar coordinates, but it would be really helpful to see the diagram that I posted converted to your preferred approach by someone who actually knows what he is doing.

See https://arxiv.org/abs/gr-qc/0104077 figure 9 in particular.

Note that in radar coordinates the traveling twin's world line in the home twin's frame (figure 1) is not the mirror image of the home twin's worldline in the traveling twin's frame (figure 9). That is one clear asymmetry between the twins. If you used a different method for constructing the traveling twin's frame then you would get a violation of the second postulate which would be another clear asymmetry.

 

[Freixas]

Those are a pathology of the "naive" approach to constructing a non-inertial frame.

Thanks. I felt that the observations made in post #10 were artificial, but didn't have the knowledge needed to phrase my objection properly.

See https://arxiv.org/abs/gr-qc/0104077 figure 9 in particular.

This paper is familiar; I remember trying to understand it some years ago when you referenced it in a different thread. Maybe it will make more sense now.

Appreciate the help from everyone.