The Mandelbear's Musings

I was all set to start another curmudgeon post today, except that I read about "A massive change" and fell down a rabbit hole. Tl;dr: everything you think you know about the metric system has just changed completely. You won't notice the difference.

You probably know at least a little about the history of the metric system. Developed during the French Revolution, it was based on the unit of length, the mètre ("meter", in the American English familiar to most of my readers), which was defined as one ten-millionth of the distance between the north pole and the equator on the meridian passing through Paris. The gramme was defined as the weight of a cube of pure water with sides of one-hundredth of a metre and at the temperature of melting ice. Or in more familiar terms, the weight of a cubic centimetre of water. The French philosopher Marquis de Condorcet called it a system "for all people for all time".

The intent was for the system to be based on unchanging physical phenomena. That didn't last. It's really hard to use the Earth as a reference, so in 1795 a brass metre bar was constructed, and in 1799 two platinum reference objects were manufactured, the mètre des Archives and kilogramme des Archives. (The standard metre was found to be about 0.02% short, meaning that the standard was now based only on a couple of chunks of metal.) New reference objects were created in the 1870s.

I'm going to skip ahead to 1960, when the metre was redefined by the eleventh GCPM (Conférence Générale des Poids et Mesures) as exactly 1,650,763.73 wavelengths of the orange-red emission line in the electromagnetic spectrum of the krypton-86 atom in a vacuum. That conference also defined the rest of the International System of Units (SI, from Système international (d'unités). In 1967 the 13th CGPM redefined the second, which had been defined in 1958 as 1/86400 of the year 1900, as 9192631770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium-133 atom.

The nice thing about that definition of the second is that it can't change. That made it possible to redefine the metre, as the distance light travels in 1/299,792,458 of a second. The speed of light in a vacuum isn't going to change, either. That leaves the kilogram.

All the units of the SI are derived from a small number of base units: the metre for length, the second for time, and the kilogram for mass, as well as the ampere for electric current, the kelvin for temperature, the candela for luminous intensity, and the mole for amount of substance.

I've always been kind of intrigued by the mole, which is defined as the number of atoms in 12 grams of pure Carbon-12 (Avogadro's number). Or rather it was defined...

Anyway, of the other base units, the ampere and the mole have definitions that depend on the kilogram. The kelvin, defined as 1/273.16 of the thermodynamic temperature of the triple point of water, doesn't, but it's also rather hard to measure precisely. The candela has a precise definition, but since it's in lumens per watt it depends indirectly on the kilogram.

All that changed yesterday with the new definitions voted in by the 26th CGPM (which take effect May 20, 2019).

The new definitions all result from defining exact values for various physical constants, rather than things that have to be measured. Specifically, the newly-defined constants will be:

• The Planck constant h is exactly 6.62607015×10^−34 joule-second (J⋅s).
• The elementary charge e is exactly 1.602176634×10^−19 coulomb (C).
• The Boltzmann constant k is exactly 1.380649×10^−23 joule per kelvin (J/K).
• The Avogadro constant NA is exactly 6.02214076×1023 reciprocal mole (1/mol).

There are also three that don't change:

• The speed of light c is exactly 299792458 metres per second (m/s).
• The ground state hyperfine splitting frequency of the caesium-133 atom Δν(133Cs)hfs is exactly 9192631770 hertz (Hz).
• The luminous efficacy Kcd of monochromatic radiation of frequency 540×10^12 Hz is exactly 683 lumens per watt (lm/W).

Naturally, the new defined values for the various constants have been chosen to be equal to the best current measurements of them, so there will be exactly no effect on anything you can measure outside of a lab. The whole process had to wait until the various measurements of the kilogram agreed to one part in 10^-8 (1/100,000,000).

So, finally, after just short of two and a quarter centuries, the metric system achieves the original dream of a system of measurement based on unchanging physical phenomena. It's not going to make a whole lot of difference in practice, but it's nice to know that it's not going to change any more.

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