## A Weight-Loss Problem

As readers probably know, most scientific measurements are made in metric units: specifically, the units of Le Système International d’Unités (International System of Units), abbreviated SI. (Although the US does not officially use the metric system, or SI, many familiar units are defined in terms of their metric equivalents.  For example, an inch is defined as 25.4 millimeters.) There are seven primary units in the SI:

• Meter:  length
• Second: time
• Ampere: electric current
• Kelvin: thermodynamic temperature
• Candela: luminous intensity
• Mole: amount of a substance
• Kilogram: mass

Six of these units are specified in terms of fundamental physical processes.  For example, the kelvin is defined as 1/276.13 of the thermodynamic temperature (above absolute zero) of the triple point of water.  The meter is defined as the distance that light travels in 1/299,792,458 second.

Only one of these units is defined with respect to a specific physical object: the kilogram, which is the weight of a particular cylinder of platinum/iridium alloy, stored under three bell jars in a vault at the Bureau International des Poids et Mesures [BIPM] at Sèvres, outside of Paris.  The Buzz Blog at the PhysicsCentral site of the American Physical Society has a note, based on an NPR report, that there is concern that the mass standard may be changing.  The primary cylinder itself is not used for making measurements; in fact, it has only been removed from its protective environment three times in more than a century since it was made, primarily in order to make copies that could be used as practical standards.  But comparisons of these copies against each other show that their masses are slowly drifting apart.  There are many possible reasons for this: for example, absorption of air or another gas, tiny scratches, or microscopic accumulations of dirt.

This is not a new problem; the reason the other basic units are defined in terms of physical processes is so they can be replicated without reference to a particular object.  Originally, most units were defined with reference to some object:

… the Egyptians … constructed a standard for the cubit, a length of granite preserved with a fierceness to rival even the BIPM. Architects and builders made yardsticks based on the cubit rod, and brought them back periodically to make sure they didn’t deviate too far from the cubit. This was good enough to build structures that have lasted for thousands of years.

The meter was originally defined, when the metric system was adopted by France in the 18th century, as 1/10,000,000 of the distance between the Equator and the North Pole.  (Remarkably, the measurements made in 1790 got a value that was only off by 0.02 per cent.)  Later, before the current definition was adopted, the meter was defined by a platinum-iridium bar kept in that same vault at the BIPM.  The second was originally defined as a fraction of a solar day, until better measurements led astronomers to realize that the length of a day was not constant.   After a couple of intermediate kluges, the second is defined today 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 cæsium 133 atom.   Admittedly this is not quite as snappy as saying that a second is 1/86,400 of a day, but it is presumably reproducible.

There are efforts underway, at the National Institute of Standards and Technology [NIST], to produce a definition of the kilogram that does not rely on comparisons with a physical artifact.  Their research is focused on the use of a very sensitive scale, called a watt balance, which does not depend on comparing one mass with another.

In a way, this concern about the precise definition of units is a result of our ability to measure the physical world more and more precisely.  Even the GPS, for which you may have a receiver in your car or cellphone, has to take General Relativity into account.  At least we don’t have to measure work in units of stone-barleycorns any more.