Authors: Gary Osborn
The time shown by a moving clock depends on its history. The Lorentz transform does not distinguish between the history of an accelerated clock and a constant velocity clock. The history of the clock can be assimilated by integrating the first derivative of the Thomas precession from the time t=0. A definite integral is required because the unknown trajectory of the clock in the distant past affects its displayed time. The coordinates are spinning in the second frame of reference during the integration, but in the definite integral from time t=0 to time t the spin accumulates to a specific angle. The integral is equivalent to a Lorentz transform followed by a space rotation. A space rotation does not affect the invariant quantity r2 - c2 t2. The history of a jerked clock is different than that of an accelerated clock. The solution in that order is equivalent to a Lorentz transform followed by two consecutive space rotations in different directions. Similarly, there are three rotations in the ä solution.
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