Let us consider a medium and an observer that is moving through that medium. Say that the magnitude of the velocity of light with respect to the medium is and say that the velocity of the observer with respect to the medium is . Can we construct a device that allows us to measure the velocity of the observer with respect to the medium?
We consider a simple device constructed by a measuring rod , a pulsing light source and a sensor at one end of the measuring rod and a mirror on the other end of the measuring rod . If this measuring rod is moving with respect to the medium such that is the angle between the measuring rod and the velocity of the measuring rod – then we find
This can be written as
Say the we have three measuring rods – the main measuring rod and other measuring rods at angle then we have
Now it is clear that
which allows to solve , and
which allows to solve . So we can find the speed of light with only one clock – assuming that there is some medium for light propagation. The question is if such an experiment can be performed as is very small. Once we can find the speed of light by using only one clock then we are able to synchronize two remote clocks. We may wonder what that does with the principles of Relativity?
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