We analyze here the changes that may occur in the length of a rod due to Lorentz contraction, when the rod, initially stationary in one inertial frame, is accelerated so as to come to rest in another inertial frame. The rod that earlier appeared shorter due to the Lorentz contraction in one frame should later appear shorter in the other frame. Has the rod length been reduced during acceleration, as might appear in one of the frames, or has it expanded as may seem in the other frame? What exactly lies behind the genesis of Lorentz contraction during an acceleration? Actually, the accelerations at two ends of the rod, even if applied simultaneously in one frame, may not seem so in the other frame. This, in turn, may result in a lengthening or shortening of the rod in a frame, depending upon the relative timings of accelerations applied, e.g., whether the accelerations applied at the rod ends were non-simultaneous in that frame and, if so, which end started getting accelerated earlier than the other. Of particular interest is the case where the rod transits through a series of inertial frames, with a constant proper acceleration in each successive instantaneous rest frame. The rod could then be considered to be stationary in a comoving accelerated frame. In this case, the applied acceleration may everywhere be temporally constant; however, it will spatially vary along the length of the rod. Strange though it may appear, all sections of the rod, in spite of their differential accelerations, come to rest simultaneously in each inertial frame, with no change in the proper length of the rod in successive frames.

中文翻译：

---

从一个惯性系加速到另一个惯性系时的洛伦兹收缩

我们在这里分析了由于洛伦兹收缩而可能发生的杆长度变化，当杆最初在一个惯性系中静止时，被加速以在另一个惯性系中静止。由于一帧中的洛伦兹收缩而较早出现的杆应该稍后在另一帧中显得更短。在加速过程中，杆的长度是否像其中一个帧中那样减少了，或者它是否像在另一帧中那样扩大了？加速过程中洛伦兹收缩的背后究竟是什么？实际上，杆两端的加速度，即使在一个帧中同时应用，在另一帧中可能看起来不是这样。这反过来可能导致框架中杆的延长或缩短，这取决于施加的加速度的相对时间，例如，施加在杆端的加速度在该帧中是否是非同时的，如果是，那一端比另一端更早开始加速。特别令人感兴趣的是杆穿过一系列惯性坐标系的情况，在每个连续的瞬时静止坐标系中具有恒定的适当加速度。然后可以认为杆在共同移动的加速坐标系中是静止的。在这种情况下，施加的加速度可能随处都是时间常数；然而，它会沿着杆的长度在空间上发生变化。尽管看起来很奇怪，但杆的所有部分，尽管它们的加速度不同，但在每个惯性系中同时静止，在连续的坐标系中杆的适当长度没有变化。