# No eyelashes please: The kilogram, redefined

*7 min read*

*.*Updated: 23 Nov 2018, 09:38 AM IST

The 1983 definition of the kilogram has changed. It will now be defined in terms of Planck's constant, and not the international prototype kept in Paris

The 1983 definition of the kilogram has changed. It will now be defined in terms of Planck's constant, and not the international prototype kept in Paris

The other day, I did something I am dispatched to do every now and then: bought a kilo of basmati rice. It came nicely packaged in a sealed bag. It feels about what I think a kilogram should feel like, and it’s actually labelled “1 kg", and that was enough for me. I didn’t ask that it be weighed. Even when a vendor actually weighs a kilo of something for me—apples or onions, say—I don’t think about it much. There’s a weight on one side of the balance that’s marked “1 kg", and that’s enough for me.

Nothing significant in that para, I’m sure. But now consider this: what if I used that bag of rice, or the apples, to “define" the kilogram? That is, suppose you asked me, “What is a kilogram?" What if I dug out my unopened basmati, or the bag of apples, and said: “This is a kilogram!" What would you think?

Take it further: What if we mandated that every transaction involving kilograms had to use either my rice or my apples to measure against? In other words, when you try to buy a kilogram of carrots, say, how would you react if the vendor pulls out my apples and places them on the scales as a measure? My guess is, you would be startled. You’d ask for some more credible measure, probably one of those six-sided weights with “1 kg" stamped on it in Hindi and English. Fair enough. But really, how do you know for sure that that weight is 1 kg? You’d have to measure it against another one, possibly a dumb-bell from your nearest gym that’s marked “1 kg"—but in turn, how do you know its weight is really 1 kg?

This is leading somewhere, I promise. This is leading all the way to a certain ingot of platinum that sits in a glass jar somewhere in Paris: the International Prototype Kilogram, affectionately called “Le Grand K" (“The Big K"). Since 1889, the kilogram has been defined as the weight of Le Grand K. That is, every single measure you run across that says “1 kg" — whether a hexagonal piece of black metal or the scale on which you check your svelte self daily — was once calibrated by another weight, and that one was confirmed in turn by yet another, and so on: an unbroken chain of weights that stretches from my basmati package through your vegetable vendor’s hexagonal kilogram block all the way to that ingot in Paris.

The point is, you know you’ve bought one kilogram of carrots precisely because “Le Grand K" weighs one kilogram. So if you ask, “what is a kilogram?", the real answer is “that block of platinum in Paris that weighs a kilogram". But it could also be “this lot of carrots that weighs a kilogram". In other words, we have this vaguely unsatisfying definition: a kilogram is something that weighs a kilogram. Reminds me of something the British plant science writer Jonathan Drori told me recently: a tree is effectively defined as something that looks like a tree.

This is still leading somewhere, I promise. If you, like me, find it unsatisfying that the kilogram is defined like this, and has been so since 1889, you will be overjoyed with what also happened near Paris on 16 November, just a week ago. It was the final day of the 26th CGPM—the French acronym for General Conference on Weights and Measures, which happens once every four years.

The CGPM brings together delegates from all over the world to review measurement standards and science. They seek always to improve and occasionally expand what are called the SI units—what you know as the metric system. Thus in 1907, the fourth CGPM defined the carat as 200mg, or one-fifth of a gram. The ninth CGPM, in 1948, defined a whole slew of units: the ampere, ohm, volt, watt, joule, bar and more. The 17th, in 1983, changed the definition of the metre. Like the kilogram, it had been defined in 1889, too, as the length of a one-metre platinum bar (so you might have said “a metre is that bar in Paris that is a metre long"). But in 1983, the CGPM defined the metre with reference to the speed of light, called an “absolute" in the sense that it doesn’t change.

Light travels 299,792,458 metres in a second. Thus a metre is the distance that light travels in precisely 1/299,792,458 of a second. The metre, defined.

Why the need to refer to an absolute? Because even platinum ingots stored under glass jars in a vault decay over time. Le Grand K is thought to now weigh about an eyelash less than when it was made. That may not seem like anything worth bothering about, but we live in an age where even that degree of imprecision can be critical: think miniature electronics, or laser surgeries, or carefully calibrated doses of drugs. So yes, an eyelash in a kilogram is indeed worth bothering about.

Perhaps the 1983 redefinition of the metre gives you an idea of what happened with the kilogram on 16 November: it, too, was redefined. In fact, momentum has been building for years to redefine the kilogram based on an absolute. The 1987 CGPM discussed what an alternative definition might look like. At the 2011 CGPM, there was general agreement to define it in terms of Planck’s constant, but exactly how remained to be worked out. The 2014 conference noted that there had been progress towards nailing down the new Planck-based definition, but it wasn’t ready yet. Maybe next time.

Right enough, the 2018 CGPM had a resolution drawn up which contained this clause: “the definition of the kilogram in force since 1889… based upon the mass of the international prototype of the kilogram, is abrogated."

It also had this clause: “The kilogram, symbol kg, is the SI unit of mass. It is defined by taking the fixed numerical value of the Planck constant **h **to be 6.62607015 × 10-34 kg m2/s." (That’s 662.607015 trillion trillion trillionths kg m2/s, never mind what the units mean).

On 16 November, the CGPM passed the resolution, which means that on 20 May, the world will have a new definition for the kilogram. Which leaves the questions I imagine you are asking: what is Planck’s constant? What does it have to do with the kilogram?

Most of us who study physics in school or college run into Planck’s constant when we learn about Heisenberg’s famous uncertainty principle. There are limits, the principle says, to how accurately we can measure both the position and the velocity of an object. The more precisely you nail down its position, the more imprecise (or uncertain) will be your measurement of its velocity—or actually, its momentum, which is its mass multiplied by its velocity. The smaller the uncertainty in the position, the greater the uncertainty in the momentum, and vice versa. The seesaw between these two uncertainties is captured in a simple relationship: multiply them, and the answer can never be smaller than Planck’s constant.

This makes little sense in our daily lives, of course. I can tell you pretty accurately, for example, that I’m sitting in a chair right now and my velocity is zero. I can be that accurate because I measure my weight in kilograms and my velocity in metres per second, and in those terms Planck’s constant is vanishingly tiny. But get down to the scale of an electron, which weighs a million trillion trillionth of a kilogram, and things get tricky. Measure an electron’s position merely to within the size of an atom, and Planck’s constant says the uncertainty in its velocity will be thousands of km per second—which is pretty seriously uncertain.

The role that weight plays in this uncertain dance between velocity and position is the reason Planck’s constant can define the kilogram. For let’s say you had an object whose velocity you knew to within 1 metre per second, and whose position you knew to within a tiny fraction of a metre—to be precise, to within 662.607015 trillion trillion trillionths of a metre. Planck’s constant tells us that such an object weighs 1 kg.

The kilogram, defined right there.

Of course it’s difficult to imagine measurement like that. But we actually have an instrument that can be that precise. The Kibble balance is essentially a weighing scale that measures how much electrical power we need to balance a kilogram; and in so doing, it gives us a value for Planck’s constant. Last week’s CGPM noted that the SI units are based on absolutes like the velocity of light and Planck’s constant, and listed their values as part of their resolution. So since we have a standard value for Planck’s constant, and since the metre and the second are also defined, we can define the kilogram.

And because Planck’s constant is an absolute, this kilogram, unlike Le Grand K, will never decay. Raise an entire eyebrow to that.

Once a computer scientist, Dilip D’Souza now lives in Mumbai and writes for his dinners. His Twitter handle is @DeathEndsFun