Two spaceships with string "paradox". Consider two spaceships, both at rest in our inertial frame, a distance \(D\) apart, one behind the other. There is a light string of restlength \(D\) tied between them. Now the ships, both at the same time in our frame, begin to accelerate uniformly to the right, with the string still tied between them. The ships start at the same time and have the same acceleration, so the distance between them, and therefore the length of the string, must be constant in our frame. However, we know that a moving string should be Lorentz-contracted in its direction of motion, by the usual factor \(\sqrt{1-\beta^{2}}\). Therefore, does the "need" of the string to become shorter in our frame cause it to break eventually, or does the fact that its length remains the same in our frame mean that it will not break? Explain which is correct. The "proper length" of an accelerating object can be measured by observers in an inertial frame instantaneously comoving with the object, that is, in an inertial frame that at some moment is at rest relative to the object. This "paradox" was originally posed by E. Dewan and M. Beran in 1959 and later modified by J. S. Bell in 1987."Speakable and unspeakable in quantum mechanics," Cambridge University Press, 1987, some very good physicists have gotten the wrong answer, at least initially.