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The metre was defined at the end of the $18^{th}$ century as the ten-millionth part of the quarter of the meridian (from the north pole to equator). Then, from $1983$ the definition changed for the distance traveled by light in a rather short elapse of seconds.

My question is, did the value of the metre change in absolute in 1983 ? My textbook talks about a difference of $0,229$mm (I couldn't understand if it was "in absolute" or if it was a difference between the Delambre & Mechain measured circumference and the satelite-measured circumference expressed in a fixed metre system).

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No, there was not.

The meter has been redefined multiple times, and, each time, the intent was to keep the actual length as close as possible to what it was before. Not long after it was originally defined based on the length of the meridian, it was redefined to be the distance between two marks on the official platinum-iridium meter bar in Paris. That definition stuck until 1960, when it was defined to be a certain number of wavelengths of light produced by a certain electron transition in a certain isotope of Krypton. The specified number of wavelengths was 1,650,763.73. Note that, if they were willing to allow the length of the meter to change by almost a quarter of a mm, they would have specified that number to fewer decimal places.

Finally, it was redefined to be 1/299,792,458 of a light-second. Again, they specified that many digits because they didn't want to change the length of a meter by more than a tiny fraction. In fact, they didn't want to change it at all - they just wanted to make it more precise.

At the end of the History of the meter article in Wikipedia, there is a table of the different definitions. It shows the precision of each definition, but not an absolute difference. That is because each one was designed to be within the range of error of the definition before. It is as if you bought a new meter stick with thinner tick marks than the old one, so you can make more precise measurements. But each tick mark in the new ruler is basically in the middle of the corresponding tick mark in the old ruler.

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  • $\begingroup$ Also, it is common to talk about how much a unit changed after the fact. This is common when we develop better ways to measure both the old and new unit, and can better distinguish the difference between them. $\endgroup$
    – Cort Ammon
    Feb 28 at 4:11

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