## A Generalization of the Thomas Precession, Part I

**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 r^{2} -
c^{2} t^{2}. 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.

**Comments:** 4 pages, no figures

**Download:** **PDF**

### Submission history

[v1] 2017-08-09 01:33:39

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