How can I implement a clock that can be used to synchronize another clock?
Do you mean a Clock or an animated wall clock, or some other sort of clock, like a game clock? Why do you need two clocks: cannot the output of one clock be used in multiple places? Or is one a physical clock, controlled by Mathematica?
I have a clock that is not synchronized, so I need Mathematica to show me the current atomic time so that I can synchronize it.
I feel there is something probably still missing from the description of the problem, but when I want something to show me the time, I use a cell phone or maybe my computer's clock, which set their times from one of the NIST servers. In Mathematica you can use DateString or DateList. I don't know what its source is, maybe the computer's clock.
I just want Mathematica to get the atomic time from a server and display it in real time so that I can synchronize my watch on my wrist.
Why do you need Mathematica to do this? On a Linux or Mac OS shell
Your computer is probably set to synchronize its clock with NIST so you can just do this from the shell