Okay, I think my understanding of electromagnetism is a bit off, because I don't completely understand what happens here:

Say we have two positive charges moving parallel to each other at the same velocity relative to me (the observer). I'll observe a magnetic field around each charge's path which attracts the other charge, so the charges come closer together. However, from the charges' frame of reference, since they are stationary relative to each other, won't they repel because they are the same charge?