What? That doesn't make any sense. Keeping good time isn't about agreeing with another copy of yourself. It's about agreeing with an objective reference time, like "sunrise in Singapore" or "astronomical noon".
This assumes that your own divergence from objective time is linear in the amount of time that passes.
He drove three Cesium clocks up Mount Rainier and returned after a week. He compared them to a clock he left at home for the journey. The graph that he shows on the page and his associated commentary is interesting.
Ultimately, a clock is simply an abstract device that goes tick-tick-tick at some regular rate. Once one starts measuring the phenomenon itself---mechanics of the human heart, tidal forces on the Earth, friction in a pendulum, or the uncertainty principle in atoms---it is no longer feasible to treat it as objective time.
International Atomic Time (TAI) itself consists of an ensemble of 400 atomic clocks, with the collective being more accurate (the proper word is "stable", I think?) than any of its constituents.
Yes exactly. But how would you measure astronomical noon? You might build some instruments that look at the sky and produce some readings.
Now you might build multiple copies of your instrument and compare their readings. But they disagree by some amount.
So you build a better instrument. Or choose some other thing to measure instead. Rinse repeat until you have a more precise instrument.
Atomic clocks are instruments that are measuring something in the universe. They are not generating some time stamp out of nothing. The thing that you say as an objective reference still very much applies.