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If we have two inertial frames $S$ and $S'$ and $S'$ is moving to the right w.r.t. $S$ with a velocity $v$. Suddenly $S$ undergoes negative acceleration (no longer being inertial) and after some time the acceleration stops when the frame has reversed its velocity. How much will be the time difference between two, previously synchronized, clocks in $S'$ separated by a distance $x$ (as measured by $S$) after the acceleration has been ceased and will it depend on the history of acceleration or just on the initial and final velocity?

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user56417
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1 Answers1

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In general it depends on the history of the acceleration.

For the case of constant acceleration your question can be answered quite simply, and I've described the calculation in the Q/A How long would it take me to travel to a distant star? or see John Baez's article on the relativistic rocket for a list of useful related equations. The derivation I used is described in Gravitation by Misner, Thorne and Wheeler chapter 6, but I have to say it's not very illuminating.

For an arbitary variation of acceleration with time you'd need to do the calculation numerically.

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John Rennie
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