During the journey from F1 to F0 let the co-accelerating observer have a 10 meter rod that he generally keeps aligned perpendicular to the direction of the acceleration. Every now and then he rotates the rod so that it is aligned in the direction of acceleration so he can compare the separation between the two BBs to the length of the rod. He then returns it so that it is perpendicular to the direction of the acceleration until he makes some future measurement.

Whenever he makes a measurement with the rod the measurement is essentially the same as the measurement someone does in an inertial reference frame that has zero relative velocity wrt to the co-accelerating observer at the time of the measurement. I made the acceleration rate extremely low so the bending of the rod has negligible effect.

At the start of the accelerations, the rod and the two BBs are each 10 meters apart. But when the speed of the BBs and co-accelerating observer is zero with respect to F0, everyone in F0 measures the separation of the BBs to be 5 meters apart. So when the co-accelerating observer rotates the 10 meter rod so that it is aligned with the BBs he finds that the separation between the BBs is only half the length of the rod at this point in time. He then returns the rod so that it is perpendicular to the direction of the acceleration.

David Seppala

Bastrop TX