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Let's imagine that I have two standing clocks and I sit in the middle. Sending two rays of light to both of them I can be sure that in my frame of reference they are synchronized.

If now I put them in motion, Lorentz transformations say that I do not see them showing the same time anymore. This cannot be due to time dilation effects since they move at the same velocity w.r.t. me.

Besides maths, how would you physically explain this de-synchronization phenomenon? It is something happening when I put them in motion (i.e. when I accelerate them)?

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In your reference frame you do see them showing the same time. More precisely, you might not see them showing the same time because light can take longer to reach you from one than from the other, but if you take that into account you can calculate that they are synchronized in your frame. However, they are not synchronized in their own frame, because acceleration makes the planes of simultaneity change.

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  • $\begingroup$ Could you elaborate on the point "acceleration makes the planes of simultaneity change". What I still do not see is how we can describe a difference in time between the two clocks while they are moving at the same velocity. $\endgroup$ – Arnaldo Maccarone Apr 25 '18 at 5:52

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