clocks measure time by counting events that we believe are periodic with whatever this quantity we call "time" is. so, how exactly do we decide that, whatever "time" is, there is an equal amount of it between the onsets of "periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium 133 atom"? is that an assumption regarding the stability of such radiation? or are there other natural periodic phenomena that we compare this radiation to, and discover that, to a very high degree of precision, they all have a number of oscillations that are extremely close (so close that we cannot measure or sense an error) to precisely proportional to each other (given the same and simultaneous period of counting), that we believe them all to be oscillating at their individual constant rates w.r.t. time? i think that this is essentially what any question regarding "what do clocks measure?" should mean. and if the thread was unlocked, i would have added this to that thread rather than start another.