There's a press release on EurekAlert about new measurements limiting the change in the fine structure constant from the Time and Frequency division of NIST in Boulder:
Some astronomical and geological studies suggest there might have been very small changes in the values of fundamental constants over billions of years, although the results have been inconsistent and controversial. If fundamental constants are changing, the present-day rates of change are too small to be measured using conventional methods. However, a new comparison of NIST's cesium fountain and mercury ion clocks, scheduled to appear in this week's issue of Physical Review Letters,* has narrowed the range in which one of them--the "fine-structure constant"-- possibly could be changing by a factor of 20. Widely used in physical theory and experiments, the fine-structure constant, represents the strength of the interaction between electrons and photons.
Astronomers and geologists have attempted to detect changes in natural constants by examining phenomena dating back billions of years. The NIST experiments attained the same level of precision by comparing the relative drifts in the "ticks" of an experimental mercury ion clock, which operates at optical frequencies, and NIST-F1, the national standard cesium clock, which operates at lower microwave frequencies. These data can be plugged into equations to obtain upper limits for possible rates of change of the fine structure constant in recent times.
Unfortunately this week's PRL hasn't gone live yet, and the paper wasn't posted to the Arxiv, so I can't look at the actual numbers, and won't have a chance to see them before leaving for the weekend. It's one of those technical tour de force experiments, though-- the things that group does with their mercury ion frequency standard are just amazing. And, of course, I'm a huge fan of laboratory tests of new physics, so there's no way I can let this go by without a comment, even if I can't say much.
If you want to know more about the fine structure constant, I talked about dimensionless constants a while back, and followed that up with a post on possible changes in the constant.
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Fixed alpha constrains varying-c theories in that h would have to increase inversely proportional to c. Since (alpha) = (ke^2)/hc and k = 1/(4 \pi \epsilon_0), fixed alpha constrains permittivity \epsilon_0 to be constant. Therefore if c changes permeability \mu_0 is likely to change. If c ~ t^(-1/3), then \mu_0 ~ t^(2/3) and the scale of magnetic fields expands. Fascinating to think about!