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An interesting subject.
I think, though, that an important point is being overlooked.
Visualise the impossible and simplify things a bit: A man leaves, or passes, the Earth at a steady but significant proportion of the speed of light. He is reading a book. The camera in his cabin captures his every move and transmits it via some sort of radio link. The receiving station back at his departure point records faithfully his every move (there will be a significant doppler shift in the transmission frequency, but for this exercise this can be ignored).
Let us say that, because he is reading about a complex subject or a copy of Playboy, he reads just one page per minute. So, after reading 60 pages he presses a button on his chair arm rest and then instantly returns at the same rate (I did say that this was impossible).
So, at the point he presses that button, what has the receiving station seen?
Well, assuming all the electronics are functioning correctly, it has just received an image of page 30. Why? because it takes the radio information a finite amount of time to arrive at the observation station.
What happens when our man turns back to the observation point? Exactly the same thing but in reverse. In other words his turning of the pages of his book will become closer to the one-per-minute mark but will not reach that frequency until such times as he (improbably) comes to a sudden halt or, again, speeds past our hypothetical observer.
But, but, but! Yes, by the time he returns he has indeed turned over 120 pages of his book. Both parties would agree on that. However the clock which our man wore on his wrist has recorded just two hours (one turn of the page per minute) as would be expected. The clock at his departure/arrival site though has measured double that.
Who is right? Obviously both are.
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