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?

  • $\begingroup$ Isn't the rule just $\lambda\nu=c$? $\endgroup$ – probably_someone Jun 13 '18 at 19:43
  • $\begingroup$ What do you mean by "independent"? They both measure time after all. $\endgroup$ – ACuriousMind Jun 13 '18 at 19:49
  • $\begingroup$ Well, both measure something. With "independent" I mean that we would have to establish that both measure the same time by experiment. $\endgroup$ – Harald Jun 15 '18 at 11:20

Starting with Einstein's 1905 paper on special relativity, the implicit operational definition of time has been that time is what a clock measures, and the implication of this definition is that all clocks measure the same time. Before Einstein, people had been pursuing systems of thought in which such things were explained by physical stresses in specific systems. Under such systems, there was no clear reason to think that if clock A and clock B had the same world-line, they would measure the same tim.

  • $\begingroup$ Hmm, I am afraid I don't understand how this answers my question. Both clocks measure something. Why do both methods agree? Established by experiment or inescabable math? $\endgroup$ – Harald Jun 15 '18 at 11:20

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