It seems that combining two Lorentz boosts cause rotation: https://en.wikipedia.org/wiki/Lorentz_transformation#Composition_of_two_boosts Do you think this rotation is something that could be measured by gyroscope? Or is it like space rotates around the accelerating observer, and the observer has no means to measure this rotation locally? If I get this right, we could accelerate two observers differently so that they finally have the same velocity vector (and common rest frame), and their final orientation is not the same, although the initial orientation is. So the accelerations have somehow created a difference in orientation, but can we determine, which one of the observers has performed this rotation, or how this should be interpreted? Thanks.