How to Define a Kilogram

So I recently read a great twitter thread by Max Fagin about the redefinition of the kilogram. It was on the news, and I saw a few TV segments about it, but I don’t think most appreciate the enormity of changing this basic building block of science. I learnt because if this story that there is a whole branch of science dedicated to the study of measurement, metrology. Metrologists ask and have answered the question, what actually is a unit of measurement? A weird question because we all probably have an idea in our head of what it means. If you are in the UK (or most of the world) then you would use a metre to measure distance, liters to measure volume, and kilograms to measure weight. In some parts of the world such as the USA then you may use gallons, feet, inches and pounds, but they all have to reference something. There are 2.2 pounds in a kilogram, 2.54mm in an inch but which one defines the other? Is it just a tangled mess of  interconnecting reliance?

It turns out it is not. All official units used in science (even the imperial units used in America) are defined in relation to the SI (Système International) unit definitions. They were established and have been maintained by the Bureau International des Poids et Mesures (BIPM) in France. It all starts with seven base units, and from them every other unit of measurement in existence can be defined. They are:

  • Kilogram, kg (mass)
  • Metre, m (distance)
  • Second, s (time)
  • Kelvin, K (temp)
  • Ampere, A (electric current)
  • Candela, cd (luminous intensity)
  • Mole, mol (quantity)

Every unit you have ever used is “officially” derived from these seven units. Ever used Watts? defined as 1 kg*m^2/s^3. 5 volts is officially 5 kg*m^2/(s^3*A). What about a gallon? Officially it is 0.003785 m^3. One atmosphere of pressure would seem simple enough until you realise it is 101325(kg/(m*s^2) of pressure.

Difference between the SI base units and the SI units that are derived from it. Image from @usnistgov

There is no standard foot, pound or gallon sitting in a vault in Washington or London, although they was at one point. All units are defined (also known as traceable) through the SI base units. But how do we define the 7 base units themselves? Well historically they are all based off of a thing, or artifact. For instance in the 1940’s 1 second was defined as 1/86400 the time it takes the Earth to rotate once. Then in the 1950’s it was redefined as 1/31556925.9747 the time it takes the Earth to orbit the sun. It took until the 1960’s for technology to advance far enough to redefine the second to something that isn’t an artifact (in this case the Earth). The time it takes the Earth to orbit the sun changes over time, it may be a long time, but it does change slightly. If the thing you are defining from changes, the thing you are using changes. If the Earth takes slightly longer to orbit the sun then the second becomes slightly longer. Although most of us don’t care, some very important science is based off of this very specific value.  Now it is based off of a fundamental property of the universe, something that doesn’t ever change. The fundamental property defining the second is the time it takes an electron in a cesium-133 atom to oscillate 9,192,631,770 times. As current science believes that the oscillations of electrons are constant properties of the universe the definition is now good forever.

The new caesium fountain atomic clock NPL-CsF3 becomes operational, allowing continuous operation of a primary clock at NPL. Work continues on the next generation of optical atomic clocks at NPL, which should achieve accuracies equivalent to losing or gaining one second in the age of the universe. Credit: NPL

The metre had a similarly long journey. British and BIPM spelling is metre, and American is meter. First it was defined as 1/10,000,000 of the distance from the equator to the north pole, but then they realised that the Earth surface is not consistent, and is definitely not constant. The Earth’s shape will change over time. So then they defined it as the distance between two marks on a platinum-iridium bar in France, literally an artifact. The bar was 90% platinum and 10% iridium, and was measured at the melting point of ice. This original bar is still kept under the conditions specified at it’s creation in 1889. In the 1980’s timing equipment became precise enough to move away from this artifact based definition. The constant of the universe used is the speed of light in a vacuum, 299,792,458 m/s (roughly 300 million). Basically a meter is defined as the distance light travels in 1/299,792,458 of a second. As it is constant it can be measured literally anywhere in space and time and it would be exactly the same, so a good definition. It also relies on time being measured using a constant of the universe too.


Closeup of National Prototype Metre Bar No. 27, made in 1889 by the International Bureau of Weights and Measures (BIPM) and given to the United States, which served as the standard for defining all units of length in the US from 1893 to 1960

All of the other base SI units have been defined in some way based on constants in the universe, with some being more complex than others. That is all but the kilogram, the stubborn one that has up until this point eluded redefinition. For 129 years the kilogram has been defined as the mass of an artifact stored in a vault in France. It is called the International Prototype Kilogram. Made like the metre, it is 90% platinum and 10% iridium. Unlike time and distance there is no easy way to precisely measure mass. So every attempt up until this point of redefining the kilogram has not met the precision of just taking the IPK out of the vault and giving it a good measure every once in a while. This is somewhat frustrating to metrologists as over the past 100 years there is evidence that the IPK has actually changed in mass by losing some material. It has changed by about 50 micro grams compared to it’s replicas. This is an odd paradox because it was the only thing in the universe that cannot not be a kilogram. So if some technician or scientist dropped it or chipped it then the weight we define atoms would literally go up. The IPK always weighs 1 kg. This is equally annoying because so many other measurements are based on the kilogram. The Newton for instance is defined as the force needed to accelerate one kilogram by 1 m/s^2.

Mass drift over time of national prototypes K21–K40, plus two of the IPK’s sister copies: K32 and K8(41). All mass changes are relative to the IPK.

The new way to define the kilogram is very complex, and I honestly don’t understand the details, there are better sites out there to get the details of this. Essentially it is based on the Planck constant, a fundamental property of the universe. Basically it relates the energy of a photon to its frequency. If Because you can know the energy of the photon, you can know the mass, and this is then directly related to the frequency of that photon. This means the kilogram can be defined in terms of the metre, second and a few constants of the universe. This has been hypothesized for some time, but until this point the technology has not been good enough to measure the Planck constant to a  sufficient accuracy. The best way that we currently use to do this measurement is using something called a Kibble balance, previously known as a watt-balance. It uses the electric power needed to oppose the force of the kilogram. As current, and electrical potential are already defined by constants of the universe the Kibble balance, with extensive calibration, can define 1 kilogram in terms of current. When I say extensive I do mean it, there needs to be an extremely precise measurement of gravity at that point. This extra complexity does mean that most countries are unlikely to invest in such devices, for the moment. But this is an important time, all measurements we currently know of are now based on actual constants of the universe. Gone are the days where we have to take something out of a vault to calibrate our measuring devices. 

Thank You for reading, take a look at my other posts if you are interested in space, electronics, or any other sort of history. Alternatively follow me on Twitter to get updates on projects I am currently working on.

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