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This is a follow on to a prior thread, Another circular twin paradox
Consider a train of proper length 100 at rest in an inertial ground frame. It is accelerated Born rigidly to the right on a straight track to 0.6c in the ground frame, after which is still has proper length 100 but has now ground length 80. It is then shunted onto a circular track of ground circumference 80. The front grazes the rear as the front exits the circle and returns to moving inertially to the right in the lab frame.
Is this just a circular version of the barn/pole paradox? The entire train is in the 80 circumference circle simultaneously in the ground frame. It seems consistent with Einstein's view of the circumference in the Ehrenfest paradox. On the other hand, if I analyze it from the train frame, an issue arises.
Say I treat the front as if it were momentarily at rest in a series of co-moving inertial frames (as if the circle were an polygon, with inertial frames parallel to the sides of the polygon). When the front changes direction to be at rest in the co-moving frame parallel to the first side of the polygon, the front undergoes infinite acceleration at a slight angle relative to the rest of the train. This should cause the train to deform (the front should stretch out away from the train) as in Bell's spaceship paradox. That is, the train does not just deform in the simple sense of bending. It also stretches out, as in Bell's paradox.
Would this occur? Or, by making the sides of the polygon smaller and more numerous could I reduce the stretching continually until in an actual circle there would be no stretching, so that the train would not be deformed? Then the scenario should be a circular version of the barn/pole paradox.
Consider a train of proper length 100 at rest in an inertial ground frame. It is accelerated Born rigidly to the right on a straight track to 0.6c in the ground frame, after which is still has proper length 100 but has now ground length 80. It is then shunted onto a circular track of ground circumference 80. The front grazes the rear as the front exits the circle and returns to moving inertially to the right in the lab frame.
Is this just a circular version of the barn/pole paradox? The entire train is in the 80 circumference circle simultaneously in the ground frame. It seems consistent with Einstein's view of the circumference in the Ehrenfest paradox. On the other hand, if I analyze it from the train frame, an issue arises.
Say I treat the front as if it were momentarily at rest in a series of co-moving inertial frames (as if the circle were an polygon, with inertial frames parallel to the sides of the polygon). When the front changes direction to be at rest in the co-moving frame parallel to the first side of the polygon, the front undergoes infinite acceleration at a slight angle relative to the rest of the train. This should cause the train to deform (the front should stretch out away from the train) as in Bell's spaceship paradox. That is, the train does not just deform in the simple sense of bending. It also stretches out, as in Bell's paradox.
Would this occur? Or, by making the sides of the polygon smaller and more numerous could I reduce the stretching continually until in an actual circle there would be no stretching, so that the train would not be deformed? Then the scenario should be a circular version of the barn/pole paradox.