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Say there is a Clock A at Point A and a Clock B at Point B. Points A and B are not moving with respect to one another---they are in the same inertial frame. A movable Clock C, while at rest at Point A, is synchronized with Clock A. Then Clock C moves from Points A to B. While it is moving, observers at Points A and B will observe time in the Clock C frame going slower than time in Clocks A and B. An observer moving with Clock C sees time in Clocks A and B's frame going slower than time in Clock C's frame. (Time dilation is symmetric.) Up until the very moment that Clock C stops at Point B, the C observer will see time moving slower in the A/B frame. But then, when Clock C stops, both of them should agree that Clock C is behind Clock B. How is this possible?

Basically, how is the twins paradox resolved when asymmetry does not result from a return trip frame switch (if the ship twin decided to stay at his destination rather than go back to the planet)?

Thank you!