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According to Derek Muller from Veritasium, measuring the one-direction speed of light requires synchronised clocks, and that's a problem because moving one of the clocks will slow down its time. In the example from the video, he keeps one of the clocks stationary while moving the other one 1km.

While watching the explanation I though "why don't starting both clocks at a given position, say A, and then moving them in opposite directions at the same speed, so their time dilation will be the same, and they will end up at points B and C separated by 1km while still synchronised".

Obviously, thousands of people way more intelligent than me already thought about this problem, so the probable explanation is that instad of single-handedly solving this problem my solution has an obvious flaw, but I can't see it. What is the flaw?

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  • $\begingroup$ Please supply the details of your proof that the clocks stay synchronized (in, presumably, their original frame). $\endgroup$
    – WillO
    Commented Jun 6, 2022 at 3:08
  • $\begingroup$ @WillO I believe I see your point: so what you're saying is that, despite the equation of time dilation depending only on the speed of the object, if there is an anisometry of the speed of light regarding orientation the clock moving to the left will have a time dilation different from the clock moving to the right, despite both moving at the same speed. Is that what you're saying? $\endgroup$
    – Megaptera novaeangliae
    Commented Jun 6, 2022 at 3:13
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    $\begingroup$ exactly. (adding more characters to reach minimum comment length). $\endgroup$
    – WillO
    Commented Jun 6, 2022 at 3:15
  • $\begingroup$ It's also very much not the "one direction speed of light" if they're going in opposite directions... $\endgroup$
    – Señor O
    Commented Jun 6, 2022 at 4:10

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The flaw is that you can't assume the clocks stay synchronized. Assuming they stay synchronized is equivalent to adopting Einstein synchronization, and thus adopting the convention that the one-way speed of light is isotropic.

The typical "equation of time dilation" used in relativity already makes this assumption. If don't want to assume this, then it is one of many equations that are not valid.

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