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The GFCM of 2018 noted that SI units are based on absolutes … because the Planck constant is an absolute, the kilogram, unlike the Big K, will never decline.
The other day, I did something that was sent to me from time to time: buy a kilo of basmati rice. He came nicely packaged in a sealed bag. That's what I think of a kilogram, it's actually "1 kg", and that's enough for me. I did not ask him to be weighed. Even when a salesman weighs me a kilo – apples or onions, for example – I do not think much about it. There is a weight on one side of the scale that is marked "1 kg", and that is enough for me.
Nothing important in this para, I'm sure. But now consider this: and if I used this sack of rice, or these apples, to "define" the kilogram? That is to say, suppose you ask me: "What is a kilogram?" And if I took out my unopened basmati, or the bag of apples, and said: "It's a kilogram!" What would you think?
Go Further: What if it was required that every transaction involving kilograms must use either my rice or my apples to measure? In other words, when you try to buy a kilogram of carrots, do you say how would you react if the seller took out my apples and placed them on the scale as a measure? In my opinion, you would be surprised. You would ask for a more credible measure, probably one of those six-sided weights marked "1 kg" in Hindi and English. That's enough. But really, how to know if this weight is 1 kg? You have to compare it to another device, perhaps to a 1 kg bell from your nearest gym, but in your turn, how do you know it really weighs 1 kg?
This leads somewhere, I promise. This leads to a certain platinum ingot that rests in a glass jar somewhere in Paris: the international prototype kilogram, fondly nicknamed "The Big K". Since 1889, the kilogram has been defined as the weight of Le Grand K. That is, each measure you walk through indicates "1 kg" – whether it is a piece of hexagonal black metal or the scale on which you check your slender self every day – was formerly calibrated to another weight, and this one was confirmed in turn by another, and so on: an uninterrupted chain of weights that extends from my basmati package to the block of hexagonal kilograms of your vegetable vendor up to that ingot in Paris.
The fact is that you know you bought a kilogram of carrots precisely because "The Big K" weighs one kilogram. So, if you ask "what is a kilogram?", The real answer is "this platinum block in Paris that weighs a kilogram." But it could also be "this lot of carrots that weighs a kilo". In other words, we have this vaguely unsatisfactory definition: a kilogram is something that weighs one kilogram. It reminds me of something that Jonathan Drori, a British writer specializing in plant science, recently said: a tree is defined as something that looks like a tree.
This always leads somewhere, I promise. If, like me, you find it disappointing that the kilogram is defined in this way, and since 1889, you will be delighted with what happened so close to Paris on November 16, a week ago. It was the last day of the 26th CGPM, the French acronym for the General Conference of Weights and Measures, which takes place once every four years.
GFCM brings together delegates from around the world to discuss measurement standards and science. They are always looking to improve and extend from time to time what are called SI units – what you call the metric system. Thus, in 1907, the fourth CGPM defined the carat as 200 mg, or a fifth of a gram. The ninth CGPM, in 1948, defined a whole series of units: ampere, ohm, volt, watt, joule, bar and more. The 17th, in 1983, changed the definition of the meter. Like the kilogram, it had also been defined in 1889 as the length of a platinum bar of one meter (so you could have said: "one meter is this bar in Paris which has a length of one meter"). But in 1983, the GFCM defined the counter according to the speed of light, called "absolute" in the sense that it does not change.
The light travels 299,792,458 meters in one second. Thus, one meter is the distance traveled by the light in 1/299 792 458 of a second. The meter, defined.
Why the need to refer to an absolute? Because even platinum ingots stored under glass jars in a vault disintegrate over time. Grand K is thought to weigh about one year less than when it was made. This may seem worthy of interest, but we live in a time when even this degree of inaccuracy can be critical: think of miniature electronics, laser surgeries or doses of carefully calibrated drugs . So yes, a kilo of eyelashes is really worth worrying about.
Perhaps the redefinition of the 1983 meter gives you an idea of what happened with the kilogram on November 16th: it has also been redefined. In fact, the dynamic has been on the rise for years to redefine the kilogram on the basis of an absolute. The GFCM of 1987 discussed what an alternative definition might look like. At the 2011 General Conference, a general agreement was reached to define it according to the Planck constant, but without specifying exactly how much remained to be settled. The 2014 conference noted that progress had been made in defining the new Planck-based definition, but it was not yet ready. Maybe next time.
Indeed, the GFCM of 2018 has drafted a resolution containing this clause: "The definition of the kilogram in force since 1889 … based on the mass of the international prototype of the kilogram is repealed".
There was also this clause: "The kilogram, kg symbol, is the SI mass unit. It is defined by taking the fixed numeric value of the Planck constant h to be 6.62607015 × 10-34 kg m2/ s. "(662.607015 trillion trillion trillion2/ s, regardless of the meaning of the units).
On 16 November, the GFCM adopted the resolution, which means that on May 20, the world will have a new definition of the kilogram. I imagine you ask the following questions: what is the Planck constant? What does this have to do with the kilogram?
Most of us who study physics at school or college come across the Planck constant when we discover Heisenberg's famous uncertainty principle. The principle says that there are limits to the accuracy with which we can measure both the position and the speed of an object. The more precisely you define your position, the more inaccurate (or uncertain) your measure of speed, or its moment, which is its mass multiplied by its speed. The lower the uncertainty in the position, the greater the uncertainty in the dynamics, and vice versa. The balance between these two uncertainties is captured in a simple relationship: multiply them and the answer can never be smaller than the Planck constant.
This naturally has no meaning in our daily lives. I can tell you quite accurately, for example, that I am sitting in a chair right now and my speed is zero. I can be so precise because I measure my weight in kilograms and my speed in meters per second. In other words, Planck's constant is tiny. But let's move to the size of an electron, which weighs one billion trillion trillion kilograms, and things get complicated. Measuring the position of an electron simply at the size of an atom, and Planck's constant indicates that the uncertainty of its speed will be several thousand km per second – which is quite seriously uncertain.
The role played by weight in this uncertain dance between speed and position is why Planck's constant can define the kilogram. Suppose you have an object whose velocity you knew at 1 meter per second and whose position you knew at a fraction of a meter away, to be more precise: at 662.607015 trillion trillion trillion meters. Planck's constant tells us that such an object weighs 1 kg.
The kilogram, defined right there.
Of course, it is difficult to imagine such a measure. But in reality we have an instrument as precise as possible. The Kibble scale is basically a scale that measures the amount of electrical energy needed to balance a kilogram; and in doing so gives us a value for the Planck constant. Last week's GFCM noted that SI units are based on absolute values such as the speed of light and the Planck constant, and listed their values as part of their resolution. So, since we have a standard value for the Planck constant, and since the meter and the second are also defined, we can define the kilogram.
And since Planck's constant is an absolute, this kilogram, unlike Le Grand K, will never decline. Raise an entire eyebrow at that.
Formerly a computer scientist, Dilip D'Souza now lives in Mumbai and writes for his dinners. His Twitter account is @DeathEndsFun
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