MACROSCOPE

# An Exact Value for Avogadro's Number

Untangling this constant from *Le Gran K* could provide a new definition of the gram

Illuminating *c*

A similar predicament concerning the speed of light existed until two decades ago. Although a basic premise of modern physics is that the speed of light is constant, from the early 1600s until the latter part of the 20th century, the official definition of the speed of light also varied with time.

The empirical estimates for the speed of light relied on the definition of a second at the time of the experiment (for example, in recent times, via the resonant frequency for the hyperfine transition in cesium-133, where the 10-digit integer 9,192,631,770 hertz *defines* one second), and they relied on the definition of a meter, which had evolved from being one ten-millionth of the distance from the Equator to the North Pole on the meridian that passes through Paris, to being the exact length of another single platinum-iridium artifact, a unique official meter stick. But as with *Le Gran K*, the length of the official meter-stick artifact was also changing with time, implying that the official value for the speed of light was changing with time.

On October 21, 1983, the roles of the constants expressing the speed of light and the length of one meter were reversed when the Seventeenth International Conference on Weights and Measures*defined* the meter to be the distance traveled by light in a vacuum in exactly 1/299,792,458 of a second. That eliminated the continuously changing official value for the speed of light, and since 1983 the distance one meter has been approximated experimentally using these fixed values for the speed of light and the second. The new numerical value chosen for *c* was the closest integer to the experimentally observed value, and since it was accurate to nine digits, was well within the range of experimental errors of laboratory equipment. More important theoretically, the new fixed definition of *c* eliminated the necessity of the artifact meter stick forever.

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