make useful working standards, the formal definition of the
meter became the distance between two scratches on a
platinum iridium bar, and the kilogram became the mass of
a cylinder of platinum-iridium. Both these artifact standards
have been preserved for more than a century in a vault at
the BIPM (Bureau International des Poids et Mesures) near
Beginning about 1900 with the development of
quantum mechanics, it became clear that nature has
constants that are more fundamental than the details of the
Earth. With the invention of atomic clocks, the second was
the first quantity to be redefined in terms of a fundamental
constant and is now defined as the duration of 9 192 631
770 (fcs) oscillations of the Cesium atom.
In 1983, the invention of lasers allowed the speed of
light to be defined as c = 299 792 458 m/s thus defining
The meter is the length of the path traveled by light in a vacuum
during a time interval of 1/299 792 458 of a second.
The Josephson effect (V = hƒ/2e) has connected the volt to a known frequency ƒ and the constants h and e
(e = electron charge and h = Planck’s constant). The Von
Klitzing Effect has made possible a laboratory realization of
the quantum resistance h/e2 = 25812.80757 ohms.
If we apply a Josephson voltage to the quantum
resistance, Ohm’s Law gives the resulting current I = V/R
= ƒ e / 2. Of the primary physical and electrical quantities,
all but the kilogram now has a quantum realization. The
kilogram has resisted redefinition for nearly five decades.
Even more concerning is that over the last 70 years,
the artifact kilogram in Paris appears to have lost about 50
micrograms relative to six copies that — among themselves
— are more stable. Only the kilogram is standing in the
way of a redefinition of the metric system in terms of the
fundamental constants e, h, c, and ƒces.
Think about it. At present, all our measurements
of mass depend on a comparison to some other mass
and ultimately to that block of platinum-iridium in Paris.
How could we measure a mass in terms of fundamental
constants? The first thought is Newton’s Second Law F =
MA or M = F/A.
If we could apply a known force to an unknown mass
and then measure the acceleration, we could calculate
the mass. The problem is that to be an improvement over
the artifact kilogram, both A and F should be measured to
better than about three parts in 108.
Acceleration can be measured with the required
accuracy by counting fringes from a moving mirror in a
laser interferometer. We can calculate a magnetic force
between two current-carrying coils from knowledge
of the currents and the detailed geometry of the coils.
Unfortunately, uncertainty in the geometry leads to
an uncertainty in the force that falls several orders of
magnitude short of the required three parts in 108.
In 1980, Brian Kibble suggested a beautiful way to
circumvent this problem. His apparatus is a balance scale.
On one side is the unknown mass. On the other side is
a coil that can move vertically in a magnetic field. The
balance works in two modes: calibration mode and force
In calibration mode (switch open), the coil is moved
vertically at constant speed S. From Faraday’s Law, this
produces a voltage:
V = BLS
Since V and S can be measured with high accuracy,
the product BL can be calculated BL = V / S — in effect
calibrating the apparatus without the need for a detailed
Figure 1. The golf
ball sized cylinder
that has defined
the kilogram since
Figure 2. This
and is generally
referred to as a
watt balance (BL ≈
Post comments on this article and find any associated files and/or downloads at
September/October 2018 77