[Special relativity] How can time be dilated for radio wave signals?

Question

So I came across this multiple choice question on an exam whose answer I cannot understand no matter how hard I try, and its stressing me out. This is it word for word.

Spacecraft S66 is travelling at high speed directly away from Earth carrying a highly accurate atomic clock.

An observer, E, on Earth emits a short radio pulse to spacecraft S66, which reflects it directly back towards the observer. The time elapsed for E between sending and receiving the pulse is 20.0 ms.

Which one of the following is true?

A. According to E, spacecraft S66 was more than 3000 km away when the pulse reached it.

B. According to E, the pulse took longer to reach spacecraft S66 than it did to return from spacecraft S66 to E.

C. The 20.0 ms interval measured by E is not a proper time because the radio pulse travelled away and back.

D. According to spacecraft S66, the time interval between the signal being sent and being received back by E is greater than 20.0 ms.

The answer is D, and the answer simply said "D because of time dilation" without any elaboration. Now, I assume theyre suggesting proper time is the time measured by E, and thus time for the observer in S66 would be dilated, but how can this be? Doesn't light travel at the same speed for all observers, and thus time wouldn't be distorted?

Answer 1

This problem has nothing to do with time dilation for radio wave signals. Radio waves travel at the speed of light and one basic element of special relativity is that the speed of light is constant for all frames of reference. So, the speed of the radio waves from both the perspective of E and of the S66 is "c".

What is different is the passage of time on the spacecraft as compared to E. If the same exact "highly accurate atomic clock" were in both locations and were "synched" at the start, the clock on the spacecraft would run slower than the clock on the earth (that is time dilation). That means it would take longer than 20.0 ms because the S66 clock is running slower than the clock on earth.