Special Relativity has the light clock which basically counts how often a photon goes forth and back along a fixed distance.
Our most accurate clock, defining the second (at least as of today), is an atomic clock.
These seem to be two completely independent ways to measure time and define a second. Are they really independent or are there hard mathematical rules that transform the frequencies relevant in the atomic clock into the distance covered by the speed of light?
If they are independent, how can we be sure they match up?