Hyperbolic motion tretment for Bell's spaceship experiment - Sfarti, Adrian (Array, 2009)
In Bell's "spaceship" experiment, two spaceships that are initially at rest in some common inertial reference frame, are connected by a taut string. At time zero in the common inertial frame, both spaceships start accelerating, with a constant proper acceleration a as measured by an on-board accelerometer. Question: does the string break, i.e. does the distance between the two spaceships increase? We will present two treatments, one that uses only Minkowski spacetime diagrams and a second approach that uses the equations of accelerated motion in special relativity. The latter approach allows the calculation of the distance between rockets as well as the strain force in the string as a function of proper time. For simplicity, throughout the paper, all objects (string, rockets) are considered as being Born-rigid, thus neglecting the very minor effects on the length of the objects during the accelerated motion. The subject of the Bell paradox is encountered frequently in relativity graduate courses, but a complete, realistic solution has not been published to date