As I said earlier, I have finished starting at Minkowski diagrams. Neddy, we're both right. You are right that Charlie can measure Alice aging backwards (i.e. to be travelling back in time) during periods of acceleration, and I'm right in that isn't what really happens. It's a known breakdown of SR. The acceleration Charlie undergoes is so large that you have to involve GR (this can be see through the Einstein Equivalency Principle; change the acceleration into a gravitational field, and calculate its strength; you'll find that GR is required to handle that acceleration). In GR, the entire concept of a plane of simultaneity is meaningless, and so the problem disappears there. This also appears to resolve one other problem I had with the CADO-equation: if the distance \(L\) and the acceleration (difference in \(v\)) are large enough, you run into exactly this issue. So, the CADO-equation could very well be correct (if all other problems can be resolved), where "correct" means "matching SR predictions". It's just that those predictions break down under certain conditions.