Built on Facts

How tall are you? You might give an answer in feet and inches if you’re an American, or in meters most other places. And if you give than answer, I’ll have a good understanding of how tall you are - all because we’re using the same units of measurement. In practice your ruler might be a little different from mine because of slight manufacturing defects, but your meter is probably essentially the same as mine.

Scientists have to be more precise sometimes. Precision tests of (for instance) relativity and QED require many decimal places of accuracy and so well-defined units have to be available. For instance, the meter used to be the distance between two fine scratches on a particular bar in a government vault. This wasn’t very practical because the scratches weren’t infinitely thin, and a bar can’t be kept at a perfectly constant length. So the meter was redefined as the distance that light travels in a particular tiny fraction of a second. The second was defined as some large number times the period of a particular type of light emitted by cesium atoms. So on and so forth for the other units - instead of physical objects, they were defined in terms of well-understood and mostly easily-reproducible physical phenomena.

The kilogram is the one exception. Right now, one kilogram is defined as the mass of a particular lump of a platinum-iridium alloy in Sèvres, France. Here’s its mug shot. It’s the metal cylinder at the center of the nested jars.

It’s not the ideal. Making comparisons with it is very difficult because it must be kept absolutely undamaged and clean, and furthermore the mass of it or its copies doesn’t seem to stay completely put. Making a real-world physical object behave with the required precision is simply very difficult. Scientists are looking to fix this by defining a kilogram that’s not tied to any specific physical object. They’d prefer a more reproducible and fixed definition such as that enjoyed by the meter. There’s a few approaches. One that’s been in the media recently is an atom-counting approach that works like this.

Make a perfect silicon sphere of a very precisely specified size. The mass of that ideal sphere is defined as 1 kilogram. That way any sphere made to the specification can be used as a kilogram. The difficulty with this is in the making of a sphere perfectly and accurately enough to be more reliable than the current kilogram in the bottle in France. The Avogadro Project is working on this, and they have developed silicon spheres which are perfectly spherical to within unbelievable tolerances - just a few dozen nanometers in global error, with local surface irregularities smaller than a nanometer.

Of all the approaches to a new definition of a kilogram, I like this one the best. Unlike the Watt balance which is intrinsically delineated in terms of electrical properties, the silicon sphere technique actually gives you a physical object which has a mass of one kilogram while still retaining an abstract definition based on pure physical constants.

You know, I wonder if there’s a correlation in preference of method between experimentalists and theorists. Theorists might prefer the Watt balance since there’s fewer steps between the fundamental constants and the definition than there are with the atom-counting approach. Experimentalists (like me) might prefer the atom-counting approach since it actually produces a one-kilogram object directly.

Either way, it will be nice to have a kilogram not based on a single object. The International Prototype Kilogram is a relic of a bygone age in science, and it really should be in a museum by now.