FitzGerald time dilation

On the assumption that observers in the rest frame ^Apparatus of the apparatus could not detect any change in the speed of light, it is easy to show that clocks at rest in that frame (^Apparatus) will appear to run slow relative to Absolute Time, when said clocks are monitored by observers at rest in the Aether rest frame ^Aether.

With reference to the same experiment discussed above, consider light travelling from O to B from the point of view of both frames. Frame ^Aether registers a time interval

at B. Now the apparatus rest frame ^Apparatus must have its clocks working in such a way that events O and A are synchronized to read zero. According to frame FApparatus, the light has moved over a length L, and so its clock at B must read a L

time tApparatus (B) = - . Hence Hence we immediately deduce

which is the famous relativistic time dilation effect.

The interpretation of this effect requires a more detailed analysis of the relationship between inertial frames in relative motion.

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