Here's a little special relativity puzzle that I found interesting. Say we have two particles initially at rest in a frame O and separated by a distance L. They begin to uniformly accelerate at t=0 in a direction along the line separating them, until they reach a velocity v at some time t, and then return to inertial motion. Say the first particle follows a path x(t) in O. Then since both particles undergo the same motion, the second particle follows the path x(t)+L. Thus at any time, the distance measured in O between the two particles is L. But this means that in the final rest frame of the particles, the separation has expanded to [itex]\gamma[/itex] L. What's going on? What happens to the separation as observed by the two particles during this process?