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Vampke
Hi,

I am reading the biography "Einstein's greatest mistake" from David Bodanis.

On page 39 the author explains some of the consequences of relativity by referring to (although he doesn't mention it by name) the twin paradox. He explains that someone accelerating at high speed away from Earth would see life on Earth passing by very quickly, while someone on Earth observing the man in the rocket would see him moving through time very slowly.

However, I remember reading a popular science book by some or other physician that in both cases one observer would see the other in slow motion and that it is only when one of the two makes a U-turn to catch up with the other that they have had time passing at different rates when they meet up.
Which is the correct interpretation?

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He explains that someone accelerating at high speed away from Earth would see life on Earth passing by very quickly, while someone on Earth observing the man in the rocket would see him moving through time very slowly.

It seems like this author is confused. First, the word "accelerating" is unclear: is he talking about a rocket whose engine is constantly on? Or just about someone moving at high speed away from earth, but coasting, not firing a rocket engine to accelerate? I'm going to assume the latter, because that is usually how the twin paradox is presented, and it's a much simpler case to consider.

in both cases one observer would see the other in slow motion and that it is only when one of the two makes a U-turn to catch up with the other that they have had time passing at different rates when they meet up

This is basically correct. For more details, I suggest the Usenet Physics FAQ article on the twin paradox:

Note that there is a careful distinction to be drawn between what each observer actually sees (as in, the image in each one's telescope), vs. what they calculate for the coordinates of events in their respective frames of reference. The "Doppler Shift Analysis" page in the article discusses this.

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I agree with Peter, if this is indeed how it is presented in the book, then the author is confused or not explaining himself very well. If it really was someone accelerating away from Earth and about what that person actually sees, the Earth would become more and more redshifted.

I remember reading a popular science book by some or other physician
It is likely a language barrier problem, but just to point out that a "physician" is not the same thing as a "physicist".

Vampke
Thanks for the explanation, which confirms what I thought.
The guy from the other book probably had 2 degrees ;)
Clearly I meant to say physicist