Trouble understanding Symmetries

[dako7]

I'm stumped on a question about symmetries:

Imagine you and a friend are on two separate rocket ships. According to me - standing on spacestation Babylon 5 – the two of you are moving parallel to each other at a constant speed but in opposite directions. What test would you do to confirm that you were moving (besides looking at the speedometer, of course)?

I'm kind of leaning towards there being no test to be done, but I'm not so sure. Thanks in advance.

 

[Yuqing]

This is not so much a question on symmetry. If you see your friend moving without any sort of external landmark to keep track of movement, then all you can say with certainty is that your friend has non-zero velocity relative to you. The question of whether you are moving or whether your friend is moving cannot be answered. In fact I would say the question in and of itself is entirely meaningless.