How heavy is a kilogram?
In practical terms, many of our peers would have no idea, but I’m more interested in the mathematical question: How is a kilogram defined?
When the metric system was first developed, the standard unit of mass (the gram) was defined to be the mass of one cubic centimeter of pure water, measured at its melting point 0C. That definition was quickly changed to instead involve water at its greatest density (circa 4C), but for practical usage, a prototype kilogram mass was constructed in 1799, and the fundamental unit of mass was redefined to be the mass of this platinum object, known as the Kilogram of the Archives.
An updated platinum-iridium prototype was forged in 1889, and the mass of a kilogram is defined to be the mass of this International Prototype Kilogram (IPK), kept in safe storage in a vault at the Bureau International des Poids et Mesures near Paris, France. When it was first constructed, some forty copies of the IPK were manufactured, and distributed internationally to serve as reference standards throughout the world.
On occasion, the IPK and its duplicates are brought together for comparison. After careful cleaning [necessitated by the fact that these objects are stored in an atmosphere, so they gain mass from airborne contaminants], their masses are compared to one another. At the most recent comparison (in the late 80s), it was confirmed that the standard IPK has lost mass when compared to its copies stored throughout the world. And so by definition, everything throughout the universe has gained mass.
Scientists continue to work toward a definition of mass that is independent of a physical prototype (in the way that the meter is now defined in terms of the distance light travels in 1/299792458 ths of a second, and a second is defined to be “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”). Several other units are defined in terms of the kilogram, including units of force and most of the units relevant to electricity and light measurements; uncertainty in the mass of the kilogram will reverberate throughout our standards of measurement.
I personally am relieved by these developments. I now have a suitable reply for my doctor at my next physical, when she chides me for gaining weight. “I can’t help but gain weight, doc — the weights keep getting lighter!”