The kilogram is the only metric unit still defined by an artifact. The **International Prototype Kilogram**, IPK or “Le Grand K”, is a golf-ball-sized platinum-iridium cylinder in a vault outside Paris. This year I expect the General Conference on Weights and Measures to replace the IKP by an electronic realization that balances gravitational and electrical power.

The **Kelvin **or** Ampere balance **suspends a horizontal wire loop of mass m, length \ell, and current I, by a radial magnetic field B. Integrate the magnetic force \overrightharpoon{F}=q\overrightharpoon{v}\times\overrightharpoon{B}* *around the loop to find the force balance

and solve for m. Unfortunately, \ell and B are difficult to measure accurately.

In 1975, **Bryan Kibble** proposed the calibration step of moving the current-less wire loop vertically at speed v. Integrate the force per charge \overrightharpoon{F}/q=\overrightharpoon{v}\times\overrightharpoon{B} around the loop to find the induced voltage

Eliminate \ell and B from the force and voltage expressions to find the virtual power

P = V I = v B L I = m g vin** Watts**, and again solve for m. Accurately measure voltage V by comparing to the **superconducting Josephson-effect voltage**

where K_J = 2 e / h = 0.48~\text{THz} / \text{mV} is the **Josephson constant**, n_J is the number of **Josephson junctions**, and f is their microwave frequency. Convert current I = V_R / R to voltage and resistance by **Ohm’s law**. Accurately measure resistance R by comparing to the **quantum Hall-effect resistance**

where R_K = h /e^2 = 26~\text{k}\Omega is the **von Klitzing constant**, and n_L is the number of filled **Landau levels**. Accurately measure velocity v and acceleration g using interferometers.

Hence the mass

m=\frac{VI}{gv}=VV_R\frac{1}{R}\frac{1}{gv}=n_J f\left(\frac{h}{2e}\right) n_J f_R\left(\frac{h}{2e}\right) n_L\left(\frac{e^2}{h}\right)\frac{1}{gv}=\frac{n_L n_J^2 f f_R h}{4gv}\propto h,where h=0.66~\text{zJ} / \text{THz} is the **Planck constant**. The **Kibble **or** Watt balance** thus defines mass in terms of the rate of change of a photon’s energy with its frequency.