Hey,
Quick question regarding one of the special relativity questions from the 2015 VCAA exam (Question 5) (Answer is D)
Spacecraft S66 is travelling at high speed away from Earth carrying a highly accurate atomic clock. Another spacecraft, T50, is travelling in the opposite direction to S66, as shown in Figure 1.
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.
I'm able to discount option A, but I'm having a hard time understanding why options B and C are false. I understand that at such high speeds, time dilation will occur, but how is that the 20.0 ms time observed by E is proper time? Is this because E is in the same frame of reference, space?
Also, given that this is a radio pulse, would not all observers see this travelling at the speed of light, hence making the Lorentz factor 0 and thereby time dilation undefined?
Cheers