The Corner

How Many Kilograms Does the Kilogram Weigh?

Wired has a fascinating article about “Le Grand K” — the platinum/iridium slug in Paris that is the universal prototype of the kilogram. One of the more successful byproducts of the French Revolution was the standardization of units of measure into the metric system, which initially used physical objects as standards from which all fundamental measures could be derived (the joule is defined as work needed to move one kilogram distance x over time y, and so on.) But today, every one of the fundamental metrics has been redefined in terms of a constant of physics — the second is defined by the wobbling of a cesium isotope, the meter by the speed of light etc. — save for one: the kilogram. Le Grand K still rules, which is a problem, since it’s losing weight:

Familiarly known as Le Grand K and held in a vault just outside of Paris under three bell jars, it dates back to the 1880s, when it was forged by the British metallurgist George Matthey from an alloy of nine-tenths platinum and one-tenth iridium. As a metric unit, the kilogram is “equal to the mass of the international prototype,” according to the official definition. In other words, as metrologists like to point out, it has the remarkable property of never gaining or losing mass. By definition, any physical change to it alters the mass of everything in the cosmos.

Aside from a yearly ceremonial peek inside its vault, which can be unlocked only with three keys held by three different officials, the prototype goes unmolested for decades. Yet every 40 years or so, protocol requires that it be washed with alcohol, dried with a chamois cloth, given a steam bath, allowed to air dry, and then weighed against the freshly scrubbed national standards, all transported to France. It is also compared to six témoins (witnesses), nominally identical cylinders that are stored in the vault alongside the prototype. The instruments used to make these comparisons are phenomenally precise, capable of measuring differences of 0.0000001 percent, or one part in 1 billion. But comparisons since the 1940s have revealed a troublesome drift. Relative to the témoins and to the national standards, Le Grand K has been losing weight—or, by the definition of mass under the metric system, the rest of the universe has been getting fatter. 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.

This state of affairs is intolerable to the guardians of weights and measures. “Something must be done,” says Terry Quinn, director emeritus of the International Bureau of Weights and Measures, the governing body of the metric system. . . . “You have an object made with the technology of the 19th century upon which a very large proportion of modern measurements are based—not just mass, but electrical measurements and measurements of force and heat and light.”

I’m the kind of fella who finds this stuff interesting in its own right, and am Burkean enough to be pleased that the weight (no pun) seems for the moment to be with the conservatives among the measurements crowd, and against the hasty move to redefine the kilogram in terms of a physical constant (such as Avogadro’s number). But the affair is also fascinating because it represents that rare occasion in which the real world is materially affected by something like a metaphysical dilemma.

You’ll notice that the bolded sentences assume a complex metaphysical view, specifically a simplified version of the view that names function as “rigid designators” in natural language.* The idea is that stipulating that Le Grand K weighs one kilogram fixes Le Grand K as the reference of the word “kilogram,” even if Le Grand K loses or gains weight. Thus we have the seemingly absurd conclusion that it is not the case that Le Grand K has been losing weight, it is instead the case that “the rest of the universe has been getting fatter.” Metrologists might have held the view that the definition of the kilogram was not really “the mass of the international prototype” but “the mass of the international prototype at time t,” t being the moment the international prototype became the official standard. Then it would be the case that Le Grand K was not essentially a kilogram, but that by stipulation it at time t had the property of weighing a kilogram. In other words, that the relation between the object and the measure would be one not of identity, but of property-instantiation. This would clean up that seemingly absurd consequence from above, but would also neuter the advantage of having a single object one could point to as the paradigm. Notice that this problem is only partially averted by switching the standard to a universal “constant” like Avogadro’s number, for it might still be discovered that the ratio that number describes between particle number and mass might vary under different circumstances (just as it is thought that other physical “constants” behave differently near black holes) or that there are exceptions (e.g. the discovery that some particles travel faster than light.)

Maybe Ludwig Wittgenstein, who solved so many philosophical problems by dissolving them, has the answer. In his Philosophical Investigations, he writes about the seemingly peculiar property of the Standard Metre (which has since been replaced as prototype for the meter in favor of the distance traveled by light in a given interval):

“There is one thing of which one can say neither that it is one metre long, nor that it is not one metre long, and that is the standard metre in Paris.”

I’m inclined to agree — Le Grand K neither weighs a kilogram nor does not weigh a kilogram. But that hardly solves the problem of what everything else weighs.

*If you’re not bored enough: The theory of rigid designators is the subject of continuing hot debate within Anglophone philosophy. It was developed by logician Saul Kripke in a series of lectures at Princeton in 1970, and later expanded upon in the 1980 book Naming and Necessity. Kripke was attacking the view widely held since Kant’s time that truths were neatly sorted, on the one hand, into necessary (true in all possible worlds, ‘2+2=4′ and the like) and contingent (true in this world, ‘Obama is president in 2011′ and the like); and on the other hand into a priori (knowable through reason alone) and a posteriori (knowable only through experience). Most thought that all a priori truths were necessary truths, and that all a posteriori truths were contingent truths. But Kripke purported to show that there were necessary a posteriori facts — e.g. “Clark Kent is Superman” is necessarily true because both names refer to the same individual, but it’s also a truth that has to be discovered. More relevant to this discussion, Kripke also proffered contingent a priori truths, specifically that ‘the length of the Standard Metre rod is one meter.’

Update: Yes, yes, I’m playing fast and loose with the weight/mass distinction, but nothing here turns on it.