Hi,
This is a complicated one to describe, but it's been driving me and a friend mad for a few days
Let's say a train is travelling round the Earth at almost the speed of light, and there is an observer on the train and another at the only train station. Each observer counts how many times he passes the station (i.e. orbits the Earth).
The observer at the station says the counting will last for 1 minute, and he starts and stops the train.
Let's say the person at the station counted the train pass 400 times in the minute.
So far so good, but since the train is travelling close to the speed of light, time will move slower for the train passenger, so after the minute is up outside the train, he may have only felt like he travelled for two second. Since the speed of light is constant for each observer, the train passenger will see the Earth passing by at almost the speed of light, so will see the station passing by at maybe 7.5 times a second.
If he only felt like he was in the train for 2 seconds he may have counted 15 stations, but the person at the station counted 400 passes.
Since the train MUST have passed the station a finite number of times, how many times did it pass?
We may be missing something obvious, but we can't think what it is.
Thanks for any info you can give.
Paul.