(A2-11) ① Earth and Mars are static relative to one another but both are moving relative to Cormorant, at a velocity of -0.5c. So the Earth to Mars distance is contracted in the seabird’s frame of reference:
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So the time that passes for Cormorant on the outward journey to Mars is given by:
time = distance / speed
= 4.33 / 0.5 = 8.66 minutes.
② In his own frame of reference, the time Cormorant experiences during his return journey works out the same as on the outbound leg: although he is now in a new frame of reference, the only difference is that the the velocity of Earth and Mars relative to him (u) is +0.5c instead of -0.5c. u2 is therefore the same and so, in turn is the length contraction he experiences for the Earth-Mars distance. Following the same method as in ①, the time passed is once again 8.66 minutes.
The total time passed for Cormorant, on his flight to Mars and back, is therefore:
8.66 + 8.66 = 17.32 minutes.
Comparing this with your answer to question A2-10, you can see that Cormorant and Nefertiti are (remarkably) in agreement as to the time that passes for Cormorant. Nefertiti attributed the smaller amount of time experienced by Cormorant to the time dilation that resulted from his movement relative to her, whereas Cormorant attributes it to the length contraction that results from the movement of Earth and Mars relative to him. Our analysis highlights, however, that these are really equivalent ways of quantifying the same thing.
Here's the table so far:
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