Hi, I have a problem connected with time dilation symmetry, which is supposed to be explained in a following example:
A rocket travelling at 0.8c starts from station P and is directed to station Q 864 million km away. Time taken to travel as measured by space station clocks is 60minutes.
The proper time, measured by the passenger is then 34 minutes.
But what if the observer in station Q claims he was moving and the rocket was at rest?
Imagine a long rod from P to Q with clocks placed along it at regular intervals. Observer at Q sets his watch looking at the watch on the rod that is in front of him.
When a rocket reaches him, his watch shows 34 minutes, and watch on a rocket shows 60 minutes (so, they conclude that time dilation is symmetric).
I don't understand whether the two described situations differ and if yes, how they differ. If a traveller and a stationmaster compare their watches they will see whose watch is slow - at first, it's the travellers watch and then it's the stationmaster's watch. Then, something surely must have changed, yet I don't know what exactly.