Precision Spectroscopy Of Atomic Hydrogen And Variations Of Fundamental Constants

In 2003 we have measured the absolute frequency of the (1S, F = 1, m(F) = 1) --> (2S F' = 1, m(F) = +/-1) two-photon transition in atomic hydrogen. By comparison with the earlier measurement in 1999 we can set an upper limit on its variation of (-29 +/- 57) Hz within 44 months. We have combined this result with recently published results of optical transition frequency measurements in the Hg-199(+) ion and comparison between clocks based on Rb-87 and (CS)-C-133. From this combination we deduce the limits for fractional time variations of the fine structure constant alpha/alpha = partial derivative/partial derivativet(ln alpha) = (-0.9 +/- 2.9) x 10(-5) yr(-1) and for the ratio of 87Rb and 133CS nuclear magnetic moments partial derivative/partial derivativet (ln [mu(Rb) /mu(Cs)]) - (-0.5 +/- 1.7) X 10(-5) yr(-1). This is the first precise restriction for the fractional time variation of a made without assumptions about the relative drifts of the constants of electromagnetic, strong and weak interactions.