I didn't want to derail the last thread on the sliding block, but I think I noticed something interesting. If we look at http://arxiv.org/abs/0708.2490v1 consider first the image in figure 3 and compare it to the image in figure 11. Ignore the wheels, which complicate matters, for the time being, and assume the block actually slides directly on the floor. In the first image, the middle of the sliding block is flush with the floor of the elevator, in the second it is above the floor, and only the two ends of the block touch the floor. So the two diagrams are not of the same physical situation as far as the shape of the train goes. If we assume the situation is described as figure 3, then in figure 11 the trains belly should "sag" to match the floor. The train wouldn't be "flat" in an instantaneous comoving frame. If we assume the situation is as described in figure 11, the drawing in figure 3 would have to change. The train would have to be bent in an upside-down U shape, in order for its middle to be above the floor. This behavior does not seem Born rigid at all. But maybe it doesn't have to be... 1) If we imagine actually taking a flat block and pushing on one end to slowly accelerate it horizontally across the floor of the elevator, which figure represents the physical situation when we are done? (I think it should be figure 11, with the train flat in its own frame, and in the elevator frame with the belly of the train raised above the floor of the elevator). This leads to 2 2) We note that the train is rotating relative to a gyroscope after it's accelerated, where it was previously not rotating relative to a gyroscope before its acceleration. This suggest to me that the motion described above ("gentle horizontal acceleration") isn't a Born rigid motion, even though at first glance it appears to be linear.