Time dilation test
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Two observers agree to test time diliation. They use identical clocks, and one observer in frame s' moves with speed v=0.6c relative to the other observer in s. When their origins coincide, they start thier clocks. They agree to send a signal when their clocks read 60 minutes and to send a confirmation signal when each receives the other signal. (a) When does the observer in s receive the first signal from the observer in s'? (b) When does he receive the confirmation signal? (c) Make a table showing the times in s when the observer sent the first signal, received the first signal, and received the confirmation signal. How does this table compare with one constructed by the observer in s'?
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SOLUTION.
First, lets keep in mind that time flows differently in each of the frames S and S'.
a) So, the observer in S' sends the signal when HIS clock reads 60 minutes. Due to time dilation, in frame S an amount of time passed is:
60 minutes / sqrt(1 - 0.6^2) = 60 minutes / 0.8 = 75 minutes.
By that time, the observer in S' is at a distance:
0.6c * 75 minutes = 45 light minutes,
and the signal travels back to the observer in S at the speed of light c and it will take it 45 minutes to reach him. So, altogether, the observer in S will receive the ...
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