Assume two inertial clocks that were synchronized at the same location to read a certain time one hour ago and moving in opposite directions. At some point during that hour, they instantly reversed direction and did so at the very same moment. Both had undergone precisely the same acceleration resulting in their, then, advancing towards each other at the same speed at which they were originally moving apart from each other (therefore, neglect the effects of acceleration since they would be equal for both clocks). If, one hour later according to our "stationary" clock, we could observe the "moving" clock just as it passes our "stationary" clock, would it show the same time as our "stationary" clock, or earlier time or future time. And the same question except the "moving" clock is advancing towards us (has not yet passed us). And, finally, the same question except the "moving" clock is receding from us (after passing us).
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If the arrangement is reciprocal, so both clocks start together, accelerate at the same rate in opposite directions, then reverse their course in the same way, when they re-meet they will show the same time.
When the clocks are apart, each will be time-dilated in the frame of the other. However, you need to understand that time dilation is a synchronisation effect- so it will only show if you compare the reading on one of the clocks with a third adjacent clock in the frame of the other. Read any of my many other answers on time dilation if you want a proper explanation of that.
Professor Sushing
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