There are three inertial reference frames: F0, F1 and F2. F1 is moving along the x-axis in the negative x direction with respect to F0 with a speed V = sqrt(3)/2*c. F2 is moving along the x-axis in the positive x direction with respect to F0 with a speed V = sqrt(3)/2*c.

In frame F1, there are two BB's at rest positioned along the x-axis 10 meters apart as measured by observers in F1. Per relativity observers in frame F0 measure the separation between the BBs to be 5 meters. At time t0 observers in frame F0 simultaneously start the acceleration of each of the two BBs in F1. They accelerate at a constant rate and continue at this constant rate until they have zero velocity with respect to frame F2.

Using relativity concepts observers in F0 always measure the separation between the two BBs (center to center) to be 5 meters throughout the journey from F1 to F2. Observers in frame F1, observe that one BB started accelerating before the other BB. They observe that during the journey from F1 to F2, the two BB's move closer and closer to each other. Per relativity observers in frame F2 observe that the BBs were initally just under 1.5 meters apart (as measured in frame F2) before the acceleration started and when the acceleration of each BB started their acceleration was in the opposite order so the BBs move further and further apart (as measured by observers in F2) in their journey from F1 to F2 until they are 10 meters apart when they reach F2.

Everyone agrees that is the correct result of relativity. But what is puzzling is what a co-accelerating observer traveling with the BBs measures during the journey from F1 to F2. The acceleration rate has negligible effect on the separation measurements made during the journey just described , but in discussing this scenario with others there seems to be concerns how the acceleration affects the measurements made by the co-accelerating observer traveling along with the BBs on the journey from F1 to F2. So we'll make the acceleration rate very small, say a constant 0.0001 g (as measured in F0) so that it becomes self-evident that the acceleration rate has a negligible effect on the measurements made by the co-accelerating observer.

Now the co-accelerating observer has a 10 meter measuring rod that he generally keeps perpendicular to the x-axis and direction of acceleration. Before the acceleration starts he rotates the rod so that it is aligned with the x-axis. Let's say it takes him 1 second to rotate his measuring rod. He measures that the separation between the BBs is the same length as the 10 meter measuring rod. He then rotates the rod back so that it is once again perpendicular to the x-axis (and thus perpendicular to the direction of motions between the frames in this scenario). Now the acceleration starts. Just after both BBs start accelerating, the co-accelerating observer once again rotates the rod so that it is aligned with the x-axis. He observes that the separation between the two BBs is slightly less than 10 meters. After the measurement he once again returns his measuring rod perpendicular to the x-axis.

Every now and then the co-accelerating observer rotates his measuring rod to align with the x-axis to measure the distance between the BBs. As he travels from F1 to F0, he measures that the separation between the BBs is getting smaller and smaller. When he has zero velocity with respect to F0, he measures that the BBs are only 5 meters apart. But as the co-accelerating observer and the BBs continue their acceleration from F0 to F2, the co-accelerating observer measures that the separation between the BBs is now increasing with each measurement instead of decreasing. When the co-accelerating and BB's have zero velocity with respect to F2 and the acceleration has stopped, the co-accelerated observer measures that the BB's are once again 10 meters apart.

The puzzling question is what caused the BB's to move toward each other during the first half of the journey as measured by the co-accelerating observer and then move away from each other during the last half of the journey? There was no change in the direction of the force on the BB's, the acceleration pattern was identical throughout the journey (although per Einstein, the frames do not agree on which BB started accelerating first), accelerometers next to each BB did not show anything that would cause the BB's to move toward each other during the first part of the journey and then start moving away from each other during the last part of the journey. All the measurements made were simple mechanical measurements.

So how do physicists explain this phenomena? Any insights would be appreciated.

Thanks,

David Seppala

Bastrop TX