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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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  • $\begingroup$ Are both clocks accelerating to come back together? Is one of them the "stationary" clock? $\endgroup$
    – BowlOfRed
    Jan 23, 2023 at 8:14
  • $\begingroup$ @BowlOfRed : Yes to both of your questions. $\endgroup$
    – user150908
    Jan 23, 2023 at 17:42
  • $\begingroup$ Then I don't understand. How is one of the clocks both accelerating and stationary? $\endgroup$
    – BowlOfRed
    Jan 23, 2023 at 17:52
  • $\begingroup$ My recent answer to physics.stackexchange.com/questions/746656/… might help. This old one might also help: physics.stackexchange.com/questions/402683/… $\endgroup$
    – robphy
    Jan 23, 2023 at 18:03
  • $\begingroup$ @BowlOfRed : Stationary is only with respect to the observer's own frame which is not absolute. There's another frame where both frames in my example can be observed as moving - and a frame from which they're moving at the same speed. It is in this frame where the speed of each is changed (accelerated by equal amounts). Even from the perspective where one frame (our frame) appears stationary, the change in speed (acceleration) happens subsequently (re-read my example). So this frame would no longer be stationary even though it's still our frame because motion due to acceleration IS absolute. $\endgroup$
    – user150908
    Jan 23, 2023 at 19:34

1 Answer 1

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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.

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  • $\begingroup$ Comments are not for extended discussion; this conversation has been moved to chat. $\endgroup$
    – Buzz
    Jan 25, 2023 at 21:53

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