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In Special Relativity - Is their a definition of "synchronizing" clocks which are moving relative to each other?

I suspect such a definition makes no sense - as moving clocks belong to separate reference frames and there is no sense is talking about clocks and synchronization outside the context of a particular reference frame, am I correct?

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How could you synchronize them, when each frame says the clocks in the other frame are running slower? Also, there's no intrinsic chronological order of events that have space-like separation.

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Yes, I believe you are correct. I'm not an expert on relativity, but it is my understanding (from reading Einstein's book "Relativity- The Special and the General Theory) that the main value of synchronizing clocks is for clocks that are within a single inertial frame.

Hope this helps.

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You could only synchronise them for an instant, after which they would immediately go increasingly out of synch. The point is that time itself in one frame is out of synch with time in another moving relative to the first.

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The notion of synchronization in special relativity has a specific sense which is related to a specific phenomenon of the twin paradox.

When two spaceships are starting from point A and receding one from the other, each spaceship will measure the time of the other spaceship running slower than the own clock. The reason for this phenomenon is that the time dilation of special relativity is related to the relative velocity, and there is the principle that moving bodies are aging slower. (Example: A shuttle bus driver will age slower than a prisoner, even if the difference is very small).

The velocity of each spaceship - from its own point of view - is always zero (the spaceship is always its own reference point), and the other spaceship is considered to be moving at the relative velocity, so it is considered to be aging slower.

This contradiction is cancelled when both spaceships are meeting - their clocks are synchronized and may be compared. It is the same situation as the twin paradox where one twin is traveling through space near speed of light and one twin is staying on Earth. When the traveling twin comes back, they may realize that the twin who stayed home is three years older and the traveling twin only two years older.

As long as the two space ships are not meeting, their clocks cannot be compared, and each of the space ship considers that itself is at rest. When they are meeting, both spaceships traveled from A to B, but it is their path which is decisive for their respective aging, and the synchronization is done by the means of the path integral of their respective velocity. The spaceship with the higher path integral of velocity has aged less than the other spaceship.

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  • $\begingroup$ Thank you, @PM 2Ring, I corrected the phrase. $\endgroup$
    – Moonraker
    Commented Jun 11, 2019 at 18:04

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