How did the whole world end up agreeing on what time it is?
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By locations of stars. Noon is when the sun reaches the highest point in the sky.
Eventually more stars were used (ephemerides.) Astronomers were very involved with this.
Then physicists got involved and learned a second can be defined by a constant found universally in nature–atoms. The second became the most precise SI unit as a result… so precise in fact that seconds needed to be added or removed on occasion (leap seconds) to avoid seasonal drift.
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