Is there like a master ruler? Who decided what a length a cm, mm and inch would be and why?
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So, this is fun. I’m going to talk about mass instead of length, because its what I have experience in, but the process was/is very similar.
About 15 years ago i worked in a laboratory that did environmental testing. We would get samples in from construction or clean-up sites and test for specific contaminates (heavy metals, gas, diesel, etc). In the lab we had a set of weights that we would use to calibrate our scales every day, and those weights were traceable back to the “master” weights.
every year, our weights would get sent out to a calibration lab. That lab would verify our weights were still accurate. They did that by comparing them to a set of weights they kept for the purpose, which in turn were sent out every year to be compared to another set, and to another set. This would eventually lead back to the Master Weight.
All of those sets had paperwork that would trace back to the master weight, so the set was said to be “traceable”
As others have said, nowadays weights are not defined by a physical sample, but by a mathematical standard. Here is an article from 2018, when it was decided that the definition of the Kg would change, which offically happened in 2019.
[New kilogram standard: how the SI unit of mass is being redefined – Vox](https://www.vox.com/science-and-health/2018/11/14/18072368/kilogram-kibble-redefine-weight-science)
When I visited Glasgow I saw an official measuring unit, I can’t remember if it was a foot, metre, or something else, on the side of a historic building. So yeah there used to be master rulers. Same for weights as well.
There is literally “the ruler”
It burned up a few hundred years ago and so we base our measurements on true universal constants now, like the speed of light.
But for a long time we literally had “the ruler”
Inbreeding, prejudice, and if you ask the French, liberal use is the guillotine, keeps most rulers standardized.
The traditional definitions of the units in the International System (S.I., from its French initials) are interesting and occasionally useful. A meter was supposed to be the distance from a pole to the equator along a meridian divided by 10,000,000. A second was a day divided by 24*60*60. A kilogram was the mass of 0.001 cubic meters (a.k.a. 1 liter) of pure water at a temperature of 4°C (the pressure matters very little, but the definition probably specified it as 760 mm of mercury or something; I didn’t look it up but you can).
For a while there was a master kilogram and a master meter, so people wouldn’t have to go measure Earth every time they wanted to calibrate an instrument. Unfortunately those references weren’t completely constant over time and new definitions were needed. The rotation of the Earth is also not constant enough to serve as the basis for defining the second.
These days the second is defined by fixing the frequency of the photons emitted by some transition in a cesium 133 atom to a particular value, the meter is defined by fixing the speed of light to a particular value and the kilogram is defined by fixing Planck’s constant to a particular value.
Many other units are derived from these three: A newton is the force that would accelerate 1 kilogram by 1 meter per second per second; A joule is the energy spent when displacing an object by 1 meter by applying a force of 1 newton; etc.
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Originally it was decided that the metre would be one ten millionth of the distance between the equator and the north pole. Which seems quite reasonable, but it’s realistically rather hard to actually measure accurately.
So instead it was decided to make a reference metre – a metal bar that would be officially decided to be one metre long, so they did.
One they had the official metre, standardising rulers becomes pretty simple – you just compare their length to the reference metre and make sure they match.
In reality it wasn’t quite so simple, as if anyone could walk in of the street, grab the official metre and use it to measure things, it runs the risk of getting damaged or worn down over time and changing length, which would make measuring rather awkward if the length of a metre occasionally shrunk. Instead a select few groups were allowed access to make their own reference metres, those second generation metres were then taken off to various locations and used as a reference to make a third generation metres, which were used to make a larger number of fourth generation metres and so on.
This means that at the highest level, only the biggest and most important government/scientific bodies would ever get access to the highest level reference metres, with more references being made available as they go down the generations and the accuracy theoretically gets a worse tolerance. This means if you want to do high end scientific work, or something like manufacturing high grade measuring equipment it is worth paying the large sums needed to access a low generation reference metre, if you are making mid range tools like a nice quality ruler you could pay less for access to a lower generation reference, and if you are making basic tape measures or school rulers, you can use pretty much whatever as your tolerances will be pretty loose anyway.
So how do we keep rulers standardized? We compare them to the standard reference metre.
Of course it was decided that perhaps basing an entire system of measurement on a metal rod might have its limitations – what happens if someone drops it and damages it? Or how do you use it to accurately measure tiny fractions of a millimetre? And it’s is a bit awkward that if the bar gets warm and the metal expands slightly, the length of a metre changes so it is now temperature specific. So they found a better and more consistent way of starting what a meter is, which is the distance light will travel over a very specific period of time (1/299792458th of a second to be exact).
We do still use the same system of reference metres though, just based on a slightly different standard than picking one specific bar and deciding that it would be exactly a metre.
Every country had a crown, robe, and fancy chair hidden somewhere. We all decided that whomever would receive all the responsibility for the bad shit societies did within a certain area on the world map needed to always wear the crown and robe while sitting in the fancy chair. It worked so we kept doing it.
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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