Travelling Pulses

Consider two identically constructed clocks AB and CD, which are characterized by the same frequency shift factors $k_{AB}$ and $k_{BA}$:

$$\begin{array}{c} k_{AB}=k_{CD}\\ k_{BA}=k_{DC} \end{array}$$ (18)

Each of Figures 7 and 8 is an example of the spacetime history of two such clocks.

Let e.m. pulses from the first ticking clock enter, by partial transmission, the empty cavity of the second clock, which is initially not ticking (no e.m. pulse inside). Then these entering pulses will start a ticking process in this clock. Because of Eq.(21), this process is in perfect synchrony with the impinging pulses. They come precisely at the right moment and have the right phase so as to augment the interior pulse amplitude from one tick to the next . As a result, CD starts ticking in sympathy with AB.

If there is no event horizon between the two clocks, then the process can be reversed, and AB ticks in sympathy with CD. When both processes happen simultaneously, we say that the sympathetic resonance of AB and CD is mutual. In that case the pulses carry information both ways. This allows the synchronization of the two identically constructed clocks.