National Physical Laboratory

Testing the Invariance of Fundamental Constants

Time variation of the fundamental constants is a manifestation of the violation of Einstein’s Equivalence Principle required by theories uniting gravitation with the strong and electroweak interactions. The coupling constants of these interactions, the fine structure constant α and the strong interaction coupling constant αS, are not expected to vary independently. Indeed, various unification theories predict a rate of change of αS an order of magnitude or more greater than that of α.

Searches for variations of fundamental constants involve dimensionless constants, which are independent of the system of units employed. Examples are the coupling constants α and αS. In practice, limits to variation of the strong interaction are obtained through placing limits on nuclear g-factors and the electron-proton mass ratio me/mp.

The interpretation of measurements of, or limits to, time-variation of the fundamental constants over cosmological time-scales using astrophysical or geophysical data is currently open to debate. Laboratory tests based on comparisons between atomic frequency standards can provide competitive sensitivity to changes in fundamental constants. This is because, despite the much shorter timescales, a very high level of accuracy is achievable. Furthermore, systematic effects can be well controlled in such experiments and their interpretation is much more straightforward.

The frequencies of the atomic transitions used for optical frequency standards are determined mainly by the electroweak interaction. Microwave standards, by contrast, are based on transitions within ground state hyperfine structure, which depend on the strong interaction as well as the electroweak interaction. Measurements of the ratio of the frequencies of two microwave standards, or an optical and a microwave standard, over time, will provide a limit to variation of a combination of the nuclear g-factor, me/mp and α.

However, absolute frequency measurements of optical frequency standards can provide an unambiguous limit to variation of α. Transitions in different atoms or ions have different sensitivities to variation of α. By combining limits to the time variation of the absolute frequency of two or more different optical frequency standards, a limit to time variation of α can be obtained. Data available to the end of 2006 indicates that α is not currently changing by more than 4 parts in 1016 per year[1].

As optical frequency standards improve beyond the uncertainty of caesium primary frequency standards it will become preferable to measure the frequency ratios of optical standards directly in the optical domain. Direct comparison of optical frequency standards, such as those based on the 171Yb+ octupole and quadrupole transitions, is expected to yield a limit on present day, local time variation of α at the part in 1018 per year level. The 171Yb+ octupole transition has the largest sensitivity to variation of α of any transition currently used for an optical frequency standard.

  1. S.N. Lea, "Limits to time variation of fundamental constants from comparisons of atomic frequency standards", to appear in Rep. Prog. Phys. 70 1473-1523 (2007).
Last Updated: 17 Jun 2013
Created: 11 Aug 2007