Synchronize Clocks in Relative Motion: How & Why

[exmarine]

Is there any way to synchronize two clocks already in relative inertial motion? If so, how? And I am not sure exactly what “synchronize” would mean in that context. Maybe it would mean that their readings, or at least their running rates, would match when their relative motion was stopped? There would be two ways to stop the relative motion, would both have the same effect?

 

[Ibix]

You can make the tick rates match in one frame. You just shorten the pendulum of the moving clock by a factor of $\gamma$. Then it ticks every $1/\gamma$ seconds in its frame which time dilates to every second in the other frame.

But viewed from the frame of the modified clock, the the unmodified clocks tick slow. And ones in different places won't show the same time even once you correct for the lightspeed delay. However, the will always happen to show the correct time as you pasd (or at least a constant offset).

 

[Herman Trivilino]

Is there any way to synchronize two clocks already in relative inertial motion?

Make the clock-readings match as they pass by each other.