Skip to main content
U.S. flag

An official website of the United States government

Official websites use .gov
A .gov website belongs to an official government organization in the United States.

Secure .gov websites use HTTPS
A lock ( ) or https:// means you’ve safely connected to the .gov website. Share sensitive information only on official, secure websites.

Bridging classical and quantum mechanics



Darine El Haddad, Frank C. Seifert, Leon S. Chao, Shisong Lee, David B. Newell, Jon R. Pratt, Carl J. Williams, Stephan Schlamminger


Using a watt balance and a frequency comb, a mass-energy equivalence is derived. The watt balance compares mechanical power measured in terms of the meter, the second, and the kilogram to electrical power measured in terms of the volt and the ohm. A direct link between mechanical action and the Planck constant is established by the practical realization of the electrical units derived from the Josephson and the quantum Hall effects. By using frequency combs to measure velocities and acceleration of gravity, the unit of mass can be realized from a set of three defining constants: the Planck constant h, the speed of light c, and the hyperfine splitting frequency of 133Cs.


El, D. , Seifert, F. , Chao, L. , Lee, S. , Newell, D. , Pratt, J. , Williams, C. and Schlamminger, S. (2016), Bridging classical and quantum mechanics, Metrologia, [online], (Accessed May 18, 2024)


If you have any questions about this publication or are having problems accessing it, please contact

Created September 28, 2016, Updated October 8, 2019