Relativity Q: Dick & Jane Twins - Signals Received?

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In the discussion about Dick and Jane, twins separated by a space voyage, key questions arise regarding the relativistic effects on signal reception. Dick travels at 0.8c to a star 20 light-years away, leading to confusion about whether the distance is measured in Jane's or Dick's frame of reference. Both twins send out annual radio signals, prompting inquiries about how many signals each receives and when they can count them. The conversation highlights the complexities of time dilation and simultaneity in relativity, emphasizing that both should ultimately count the same number of signals despite differing perspectives. The discussion reflects the intricate nature of analyzing scenarios involving relativistic travel and communication.
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How would you make the first move in this type of question:

Dick and Jane are twins. Dick goes off on a space voyage at a speed of 0.8c to a star 20 light-years away, while Jane stays behind on Earth. Dick and Jane each send out a radio signal once a year while Dick is away. How many signals does Dick receive? How many does Jane receive?
 
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First off, is the star 20 light years away according to Jane's reference frame or Dick's? Secondly, after how long and according to whose frame do they count up the signals? Anyway, they should both count the same number of signals.
 
hmm... you're right~
wow! you ask some pretty good questions~
 
@@a
that's getting hard to analyze...
 

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