# Time dilation test

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 Preview

... signal in:
(75 + 45) = 120 minutes = 2 hours.

b) Lets calculate first when the observer in S' receives the first signal. He is moving at a speed of 0.6c away from the observer in S, and the signal is moving at the speed of light c, so the relative speed is:
c - 0.6c = 0.4c.
The observer in S sends his first signal after 60 minutes by his clock, by that time the observer in S' is
0.6c * 60 minutes = 36 light minutes
away from the observer in S. So the first signal will reach the observer in S' after amount of time equal to:
36 light minutes / 0.4c = 90 ...