Is there like a master ruler? Who decided what a length a cm, mm and inch would be and why?
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Yes, the name of the science that studies this is metrology and one of the key concepts is traceability.
Originally, there was a metal bar in France that was set to be a meter, and everything was based from it.
France gave copies to every country’s metrology institute, for example NIST in the USA. Then they made copies and gave them out through the USA, if you’re a ruler factory you might be interested in buying a certified copy.
After some time, each of the original copies where send back to France to recalibrate them, and they saw that every copy changed in a different way, some were longer, others smaller, the difference was very small of course, not even a mm, but for some applications it was enough to introduce errors in measurements. And, since everything was based on a metal bar in France, every other copy had to be adjusted to fit that specific bar.
The standard was changed to a natural constant based on properties of the things around us, in case of the meter it was how long light travels in 1/299792458 seconds.
But of course, you also have to define seconds, before it was defined from days, so 60 hours in a day, 60 min in an hour, 60s in a minute. But nowadays it is also defined of a natural property, 9192631770 vibrations of a Cesium atom.
This makes it possible for national institutes of metrology to make machines that can run this experiments and create copies of a meter right from the source, instead of basing it on an specific metal bar in France. You, as a ruler manufacturer can buy certified “meters” to calibrate your own, and there traceability all the way to the standard.
You might think that the USA does it’s own thing since Imperial units are used throughout the country, however they are now officially based on metric units nowadays, so the oficial definition of an inch is 25.4mm or 0.025m and you need a standard meter to work that out. A foot is 0.3048m and so on. In the end everything is based of metric and then converted to imperial units.
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