The measure of things





A kilogram can’t lose weight! That’s just absurd.

Here are the seven SI units and their definitions. Take a minute to appreciate them:

  • meter (the length of the path travelled by light in vacuum during a time interval of 1/299 792 458 of a second)
  • kilogram (the mass of the international prototype of the kilogram)
  • kelvin (the fraction 1/273.16 of the thermodynamic temperature of the triple point of water)
  • ampere (that constant current which, if maintained in two straight parallel conductors of infinite length, of negligible circular cross-section, and placed 1 metre apart in vacuum, would produce between these conductors a force equal to 2 × 10-7 newton per metre of length)
  • mole (the amount of substance of a system which contains as many elementary entities as there are atoms in 0.012 kilogram of carbon 12)

Notice something? Only one of these base units, the kilogram, is not defined in reference to an absolute, unchanging constant of nature. Indeed, in 1889, British metallurgist George Matthey built a cylinder of 90% platinum and 10% iridium that weighed the same as a deciliter of water. Le Grand K, as it’s known, was placed under three bell jars in a special underground vault at the Paris headquarters of the International Bureau of Weights and Measures (BIPM), and there it has sat to this very day, the definition incarnate of the kilogram.

(The image to the left is not cheese, it’s Le Grand K in its three nested bell jars, from the International Bureau of Weights and Measures website . The photo at the top of the page is a computer-generated image, from Wikipedia. Nobody ever gets access to Le Grand K to take pictures like that.)

At the time, it made sense. In 1889, the definition of the meter was one ten-millionth of the length of the meridian (through Paris, of course) from the pole to the equator. That meter was also cast in a platinum-iridium alloy and placed in the vault in Paris. But it has since been supplanted by a calculation involving the speed of light, which is immutable.

Alongside le Grand K are six identical copies, and four dozen other official replicas are located in countries around the world. As Jonathan Keats writes in Wired Magazine,

The official US kilogram — the physical prototype against which all weights in the United States are calibrated — cannot be touched by human hands except in rare circumstances. Sealed beneath a bell jar and locked behind three heavy doors in a laboratory 60 feet under the headquarters of the National Institute of Standards and Technology 20 miles outside Washington, DC, the shiny metal cylinder is, in many ways, better protected than the president.”

Once every 40 years or so, all these kilograms are assembled in France and weighed, using instruments that are accurate to one part in one billion. It’s that important that we’re all talking about the same thing when we refer to a “kilogram.”

But quelle surprise! The Paris kilogram has lost a teeny tiny bit of weight over the years. “The most recent comparison, in 1988, found a discrepancy as large as five-hundredths of a milligram, a bit less than the weight of a dust speck, between Le Grand K and its official underlings,” writes Keats.

So? Why all this protection? Why all this persnicketiness for a measly speck of dust?

Think about it for a minute. No big deal, you say? Au contraire, mon ami! The mass of the entire universe depends on it! If the kilogram loses weight, the universe gains weight. Big time. The repercussions are nothing short of mind-boggling.

The Situation is Clearly Intolerable. We cannot measure mass using a physical prototype; we need a constant of nature. There are two solutions being investigated; one involves counting silicon atoms and the other involves the Planck constant, which is some serious physics that I don’t understand and you won’t either (unless you’re Dave).

You can read about it in the lengthy Wired article, which also goes into the history of how the SI units were originally derived in France “for all people, for all time.” At one point, for example,

There were some 250,000 local units of weights and measures in France alone, many of them sharing the same names, a fact that ensured that the only constant was confusion.”

The French effort to institute standard units allowed us to take that first step down the path to globalization. Now that’s ironic, isn’t it?

When I was reading about this dilemma, it kind of rocked my world. I’d never really thought too deeply about those SI units. But now, not only did I realize that one of them was fallible, but I also realized that they were mostly defined in terms of things we were already comfortable with. Long ago we chose a fairly arbitrary set of measures with which to parse our world and do our science, and then we justified it using “a constant of nature, something hardwired into the circuitry of the universe,” as Keats so elegantly puts it.

To me, this measure of things is a perfect mélange of the subjective and objective. We categorize our world from our own viewpoint, and then fix it objectively according to the laws of the universe. If that isn’t mind-bending, I don’t know what is.

Take time, for example.

Nobody thinks about the Cesium atom when they’re reading a clock. Seconds have been used for millenia to measure time. The ancient Greeks and Egyptians divided the hour into 60 seconds. We didn’t do away with it; we just found a way to measure it that isn’t subject to the annoying irregularities of the Earth’s rotation. Using radiation from the Cesium 33 atom, you can measure time accurately anywhere without having to refer to astronomical phenomena. The recently improved NPL-CsF2 cesium fountain clock in London, for example, is so precise that it won’t gain or lose a second in more than 138 million years. That’s seriously reassuring.

Which brings me back to the leap year.

Astronomical events and seasons don’t occur in intervals separated by whole numbers of days, but calendars do, so to avoid the inevitable drift, we have to tack on a whole day once every four years to get things back on track again. As long as the second is immutable, tweaking the calendar is just fine. Science is not affected. The universe is not at risk.

That’s not to say people haven’t tried to change the calendar.  The French Republican Calendar, for example, was established the first day of the French Repulic in 1792, part of a general French obsession with all things decimal (an obsession which led, in part, to the metric system). It had 12 months, each divided into three 10-day weeks. Every day had 10 hours, every hour had 100 minutes, every minute had 100 seconds. The five or six days needed to approximate the solar year were placed at the end of the year. It was abolished after only 12 years, on January 1, 1806, by Napoleon.

This kind of thing still crops up, believe it or not. In the last issue of Reflex, I translated this snippet:

Every year, the major holidays fall on a different day of the week. School vacations, on the other hand, frequently don’t coincide. Totally ridiculous, says Johns Hopkins University astrophysicist Richard Henry. He’s rallying for a new, universal calendar, organized so that every day of the year always falls on the same day of the week. On this calendar, New Year’s Day, as well as Christmas, would always be on Sunday. To make it happen, though, we’d have to add a one-week mini-month after December once every five or six years.

In today’s paper there was a photo of a woman who is celebrating her 100th birthday today. Officially, she’s only 25. She said she was planning on skipping her gym session this morning to be fresh for the party. Happy Birthday, Renée!

For the curious, more reading on SI units:

One thought on “The measure of things

  1. Dammit, Mary, I have trouble remembering which day it is, let alone trying to check what I may weigh after a 10k run. Add all this to the fact that Americans keep referring anachronistically to mile rates, and can’t get sizes correct for their running shoes, and its all too complicated.

    Yesterday, Feb 29th, was the last day of Summer in my locale, with temperatures in the first week of Autumn predicted to be over 36 degrees Celsius (and I’m not going to convert this to Fahrenheit). At 8.15pm last night, I found myself saying good morning to a contact in Canada. Strange to think of the world being so out of sync.

    Measuring the mass of the universe may be a little difficult because of that pesky dark matter, although we’re not really sure that the stuff actually exists. Guess I need to do some research before venturing into that topic.

    Happy Sadie Hawkins day.

Leave a Reply
