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A day doesn’t last 24 hours!

Measuring time is much trickier than it looks like at first glance….
Apart from the challenges, at a “macro” level, in having a calendar (see this other post) that keeps up with the seasons (this deals with the Earth orbiting around the Sun), there are just as difficult challenges, at a “micro” level, in measuring small periods, i.e. minutes, hours or a day (this deals with the rotation of the Earth around its axis).

During the early Middle Ages, most peasants or farmers would not need to know precisely what hour it was, and would have divided their day according to the passage of the sun. Some monks, though, would have the need to organise their prayers and, adopting reference points such as dawn or sunset, the “hours” length would actually vary a lot from one season to the other….

As it happens quite often, the issue starts with the definition. For example: if we define a day as a single rotation of the planet Earth around its axis (solar day), we are exposed to the fact that this interval of time varies through the year and depends on latitude, because effects from the Moon periodically modify the speed of Earth’s rotation; the amplitude of this modification may be of the order of magnitude of a minute. On average, the solar day is a few seconds shorter that 24 hours. On top of that, the Earth rotation speed is generally decreasing: days were about 1.7 millisecond shorter a century ago. Plus, if you could observe the Earth from the stars (i.e. an “independent” reference system), you would measure a stellar day length of 23 hours 56 minutes and 4.1 seconds!

It goes without saying that, using the definition of day to derive the definition of hour, minute or second can create issues….

It is then easy to understand why, in 1967, the definition of second has changed from “1/86400th of the length of a solar day” to “the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom”. After atomic clocks principle was proved to be valuable, the first atomic clock was actually based on caesium-133 and was instrumental to the decision of changing the definition of second. With this instrument, in 2011, it has been established that the precision is so high that the clock will not lose or gain a second in 138 millions years!

These clocks have been used to prove, from a macroscopic perspective, some Einstein’s Special Theory of Relativity aspects related to the compression of time at high speeds.

Inspired by The Book of General Ignorance by Lloyd, Mitchinson & Fry.

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