THE THEORY AND PRACTICE OF CLOCK SYNCHRONIZATION FOR SYSTEMS IN RELATIVE MOTION

In the following paper we try to extend the synchronization method for situations where the two clocks are in relative motion with respect to each other as opposed to being at rest, from simple cases, like uniform, unidimensional motion to more complicated cases like rotating and/or accelerated clocks. Now, we well know, from the theory of the Global Positioning System (GPS) that the clock rate is affected by motion (and by the gravitational fields) so we are not only trying to adjust the clock rates, we are also trying to set them to the same starting time in their respective frames, notwithstanding their subsequent de-synchronization due to their relative motion. The issue we are addressing has both theoretical and practical implications, has not been addressed in prior literature and our motivation was to put together a comprehensive description of the solution. In the following paragraphs we show a few practical ways of accomplishing the synchronization of clocks in relative motion, be it uniform or accelerated. In the last paragraph we will show how to adjust the frequencies as well, once we matched the “start time”. The process of adjusting the clock frequencies, as in the GPS, in order for the clock to measure the “same time” is known as “syntonization” [1].