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.
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PAPERS| July 01 2020
Lorentz contraction during acceleration from one inertial frame to another
Ashok K. Singal; Lorentz contraction during acceleration from one inertial frame to another. Am. J. Phys. 1 July 2020; 88 (7): 551–557. https://doi.org/10.1119/10.0000964
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