The kilogram is shrinking!

No, seriously, it is. It all has to do with its definition. See, the kilogram is the only base unit in the SI measurement scheme that's based on an actual object. All of the other SI units are based on fundamental physical constants, which means they can be defined precisely, and that as measurement techniques improve, their exact values are automatically known with greater accuracy. For instance, one second is defined as "the duration of 9 192 631 770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium-133 atom." Perhaps a bit specialized, but it's a measurement that can be repeated by anyone with the requisite equipment, and the same value will be found. Same goes with the meter — one meter is defined as the distance that light travels in a vacuum in 1/299 792 458 seconds. But the kilogram is defined as the mass of a particular metal cylinder.

The prototype kilogram is stored in a vault in Paris, along with six official copies. Individual copies, termed "national prototypes", have been made for a number of countries by the Bureau International des Poids et Mesures (BIPM), the official body that defines SI units, but clearly no exact replica can be made, and so the precision of the kilogram as a measurement — which in theory should be treated as perfect — is limited by the precision of our ability to manufacture exact copies of a small hunk of metal. Further, these hunks of metal must be treated quite carefully; the BIPM's prototype and official copies are housed in individual bell jars to prevent them from wearing away or absorbing dust or gases from the air, but they can't be maintained perfectly.

And clearly they haven't been. Over the last hundred years, the prototype kilogram has lost some mass — about 50 micrograms altogether. A small amount, to be sure, but a significant one now that scales have been developed with precisions measured in zeptograms — 10-21 kg. The national kilogram prototypes are not exactly the same mass as the original, either; they are measured against it every ten years, and they measurably differ from it. This isn't enough to offer up an excuse for putting on weight, but it is a problem when it comes to very precise measurements. Since the kilogram is defined as the mass of this particular object, that means that technically speaking, if you had an object with a mass of one kilogram a hundred years ago, and its mass has stayed exactly the same since then, it now has a mass of 1.000 05 kg. Craziness!

About the prototype

The kilogram wasn't always defined as the mass of a particular object. Originally, it was defined as the mass of one liter of water at 3.98°C at atmospheric pressure, which is where water reaches its maximum density. The trouble with that is two-fold: it's difficult to measure this precisely, as small changes in atmospheric pressure will change the density of water. Further, pressure is measured with the Pascal, which is a derived unit, defined as kg/m·s2 — thus making the definition of the kilogram circular. So it was redefined in 1889: a cylinder was created out of an alloy of 90% platinum and 10% iridium, 39 mm tall and 39 mm in diameter. And the kilogram was defined as the mass of that prototype.

The choice of materials used was quite deliberate; the platinum-iridium alloy used has a density of 21.5 g/cm3, similar to that of the densest materials known, iridium and osmium, each of which weigh in at around 22.6 g/cm3. The high density means the kilogram has a low volume, which reduces the effect of buoyancy when it is weighed in air. The small surface area reduces the impact of surface contamination of the object (it has a mirror finish to further reduce the surface area), and the metals used are relatively inert which reduces — but doesn't eliminate — the accumulation of impurities from the atmosphere.

The various national prototype kilograms are compared to the original when its deemed necessary; the six copies stored along with it have been compared with it three times, along with a large number of the national prototypes, in order to assess the divergence of their masses. National copies that are used more frequently are naturally more subject to surface contamination; a careful cleaning process is used before the kilogram prototypes are used to help reduce the problem. In that process, a piece of chamois is carefully cleaned with a mixture of ethanol and ether; afterwards, the kilogram is rubbed with the chamois and solvent. Afterwards, it is sprayed with a jet of steam, carefully inverting it to expose every surface. All and all, storing, recalibrating, and maintaining these objects is a lot of work, and it introduces errors into the process constantly; in contrast, any of the other base units can be calculated to the precision of whatever equipment is used simply by knowing a definition — but to precisely determine how much one kilogram is requires physical access to either the prototype or one of its copies, and each step involved introduces more error.

A new definition

For quite some time, then, various ideas have been proposed to define the kilogram by means of some more fundamental physical constant, ideally obviating the need for comparisons with a single reference object and enabling greater precision to be used in measuring mass. There's certainly precedent for changing these definitions. The meter was first defined, during the creation of the metric system in the wake of the French Revolution, as 1/10 000 000 of the distance between the north pole and the equator on the meridian that passes through Paris. In 1889, after the establishment of the BIPM, a prototype meter was created — a bar of platinum-iridium with two lines on it, the distance being measured at precisely 0°C. It wasn't until 1960 that a standard not based upon a physical artifact was chosen.

There are four basic schemes being kicked around to accomplish this goal, and they all boil down to precisely tying the kilogram to either Planck's constant or Avogadro's number. Technically, all of these projects would involve attempting to precisely measure those two constants in relation to the current kilogram, to the limit of our ability to do so, and then setting precise values for those constants based upon those measurements. An exact definitional value for one of those constants in terms of the kilogram (indirectly in the case of Planck's constant, which doesn't directly involve mass) would conversely mean a definition of the kilogram in terms of a precise, unalterable fact describing the universe.

The Avogadro Project

The Avogadro Project aims to precisely determine Avogadro's number — defined as the number of atoms in 12 grams of carbon-12. Avogadro's number is an important concept in chemistry; it's the number of atoms or molecules in one mole of a substance, and the current best estimate for it is 6.022 135 3 × 1023. So in order to count the number of atoms in a mole of a substance, the Avogadro Project measures the precise volume of a one kilogram sphere of silicon, using silicon balls very carefully manufactured to be the roundest objects on earth. X-ray interferometry is used to determine the distance between lattice planes in the silicon crystal, permitting physicists to determine, as closely as possible, the number of atoms in these spheres. Currently, a measurement accuracy of one part in 107 is possible, after considering all of the various sorts of error introduced in the process, but it is hoped that ten times this accuracy will be possible within five years.

The Watt Balance

The Watt Balance project has provided the most accurate measurements so far. It involves suspending a coil and a one kilogram weight on opposite sides of a balance. The coil is placed in a magnetic field, and electricity is run through it. By running a current through the coil, a force is generated to counterbalance the force produced by gravity acting upon the weight on the other side. Next, the coil is moved at a constant speed, producing a measurable voltage. Thus, first an electrical "realization" of the watt is produced, and then a mechanical one. These two realizations can be related via Planck's constant, thus producing a highly accurate measurement of the number and relating it to the kilogram.

Superconducting levitation

This method works along essentially the same principles as the Watt Balance. In it, a superconductor of a known mass is placed within a superconducting coil. By running current through the coil, a magnetic field is generated that causes the superconducting mass to levitate. By levitating it at different positions and measuring the current required to do so, the magnetic flux can be calculated. Magnetic flux relates directly to Planck's constant, and because the force generated by the magnetically-induced levitation and the downward force of gravity must be equal, Planck's constant can thus be precisely related to the kilogram. The accuracy of this approach is about one part in 106, making it a less likely candidate than the Watt Balance approach. Fortunately, though, the values generated by the two experiments are similar, which suggests that these approaches are working.

Ion accumulation

Much more speculative than the three approaches listed above, the ion accumulation approach involves shooting a beam of ions — likely gold-197, though other materials can be used — at an electrode. These ions have to absorb electrons in order to become neutral again, and the amount of current spent doing so can be measured. This is a slow process — about 1.8 grams of gold can be accumulated in a day's time, which means the experiment must run for about six days to achieve the target of ten grams. By determining exactly how many electrons were absorbed in neutralizing the ions and weighing the final product, theoretically the exact number of gold atoms transmitted can be counted. Current experimentation has yielded an error of about 1.5%, making it vastly less accurate than other approaches at present.

So why are we waiting? Friggin' do it already, jerks!

The most accurate and widely-discussed efforts to define the kilogram are the Avogadro Project and the Watt Balance approach. Unfortunately, at present, their results differ from one another by about one part in 106. That means that current efforts still can't match the accuracy of the current system of reference kilograms, generally regarded as mutually accurate to within one part in 108. While it's aesthetically displeasing it is to depend upon the mass of a physical object as a definition of a fundamental unit of measurement, and while it is obvious that this definition isn't reliable over the long term, the definition of the kilogram produced by experimentation is still not as precise, and moving to a less accurate standard is obviously not desirable.

Clearly, though, a definitional value for Avogadro's number or Planck's constant could be set. That way, the kilogram would be defined in relation to a physical constant of the universe — and more precise measurements of the kilogram could be obtained immediately as progress advances in these two main efforts. The problem is that in the interim, there would be a definition for the kilogram but no one would actually know exactly how much a kilogram is! Of course, it's relatively rare that anyone measures anything within an accuracy of one part in 108 anyway; the scale at my grocery store probably doesn't measure my late-night purchases of bulk gummy worms to an accuracy of even one part in 103. Even medical science doesn't depend on this level of certainty for measurement. Mostly, this is a question of concern to physicists; having a more precise value for the kilogram would make quite a few other values considerably clearer for their purposes.

The definition of the kilogram is a major topic in the world of metrology (that is, the science of making measurements), even if it's not terribly relevant to most people. A meeting of the BIPM to continue discussing current research is planned for 2007; most likely, no new definition will be chosen, however, until these research projects are accurate enough that definitions can be formulated that simultaneously retain the current standard value for the kilogram while also relating it to a more fundamental physical phenomenon.


General information on the Système international d'unités taken from the BIPM website. (
Girard, G., 1990. "The Washing and Cleaning of Kilogram Prototypes at the BIPM". (
United Kingdom National Physics Laboratory, 2006. "Avogadro Project". (
Australian Centre for Precision Optics, 2006. "The Avogadro Project". (
Eichenberger, A., Jeckelmann, B., and Richard, P., 2003. Metrologia. "Tracing Planck's constant to the kilogram by electromechanical methods".
BIPM, 2006. "The Principle of the Watt Balance". (
United States National Institute of Standards and Technology, 2005. "NIST Improves Accuracy of 'Watt Balance' Method for Defining the Kilogram". (
Physikalisch-Technische Bundesanstalt, 2004. "Ion Accumulation Experiment". (
Mills, Ian M. et al., 2005. Metrologia. "Redefinition of the kilogram: a decision whose time has come".
Kestenbaum, David, 1998. Science. "Standards: Recipe for a Kilogram".
United Kingdom National Physics Laboratory, 2006. "Frequently asked questions — mass and density". (
I'm not sure why I love gummy worms so much.

Kil"o*gram (?), Kil"o*gramme, n. [F. kilogramme; pref. kilo- (fr. Gr. chi`lioi a thousand ) + gramme. See 3d Gram.]

A measure of weight, being a thousand grams, equal to 2.2046 pounds avoirdupois (15,432.34 grains). It is equal to the mass of a cubic decimeter of distilled water at the temperature of maximum density, or 39° Fahrenheit.

© Webster 1913.

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