74 R.S. Davis
But a molecule, say of hydrogen, if either its mass or its time of vibration were to be altered
in the least, would no longer be a molecule of hydrogen.
If, then, we wish to obtain standards of length, time and mass which shall be absolutely per-
manent, we must seek them not in the dimensions, or the motion, or the mass of our planet,
but in the wavelength, the period of vibration, and the absolute mass of these imperishable
and unalterable and perfectly similar molecules [25].
Maxwell was, of course, criticizing the original metric system, which based
the meter on a specified fraction of the earth’s circumference and the kilogram on
the mass of a cubic decimeter of water at its temperature of maximum density. The
ghost of this system is seen in our present kilogram, which agrees with this earlier
definition to within about 3 parts in 10
5
. However, “water” is not a well-defined
substance and the original definition was replaced by one based on a single, solid
artifact: first the kilogramme des Archives, and then the present international pro-
totype [10]. In some sense the density maximum of a well-characterized sample
of water is a physical constant but we no longer consider it to be “fundamental.”
This is because its properties are influenced by a number of effects that are diffi-
cult to model to arbitrarily high accuracy: isotopic abundances, dissolved gases and
other impurities, thermal expansion, compressibility, etc. The maximum density of
a particular isotopic mix of water has been determined to a relative uncertainty of
about 10
6
and this limit is not due to shortcomings of the present definition of the
kilogram.
Our understanding of which quantities in nature are fundamental constants
evolves with our knowledge. For instance, the fine-structure constant, ˛,which
today is determined by an experiment whose results are analyzed using QED per-
turbation theory [18], may one day be calculable from first principles. A possible
analogy to the value of , which in antiquity was determined by measurement,
is sometimes cited. We may one day find that ˛, or other constants, are time -
dependent (and thus not really constant) [24,35]. It may be that string theories will
lead us to revise our notions of “fundamental” constants. This paper will not enter
the debate over which constants are the most fundamental. In the following, we will
assume that the fundamental constants at our disposal are those that are listed in the
CODATA 2006 recommendation [31].
In any case, the values of all fundamental constants containing the kilogram in
their dimension must be traceable to the international prototype. How this situa-
tion is best remedied will be the subject of this chapter. Of course at some level of
precision the mass of the international prototype must be less stable than the val-
ues of the constants that are traceable to it. However, this phenomenon has not
yet been observed. A more practical concern is the experimental uncertainty in
determining such constants with respect to the present definition of the kilogram.
Thus, for instance, every time there is an improved experimental determination of
the Planck constant, its SI value changes (within the previously accepted uncer-
tainty, one hopes) and the uncertainty of the new value is improved. We will see
below that the recommended relative uncertainty of h is approximately 5 10
8
.
The relative uncertainty of the electron rest mass, m
e
, is also about 5 10
8
but the