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In an effort to resolve the discrepancy between two measurements of thefundamental constant mu, the proton to electron mass ratio, at early times inthe universe we reanalyze the same data used in the earlier studies. Ouranalysis of the molecular hydrogen absorption lines in archival VLT/UVESspectra of the damped Lyman alpha systems in the QSOs Q0347-383 and Q0405-443yields a combined measurement of a (Delta mu)/mu value of (-7 +/- 8) x 10^{-6},consistent with no change in the value of mu over a time span of 11.5gigayears. Here we define (Delta mu) as (mu_z - mu_0) where mu_z is the valueof mu at a redshift of z and mu_0 is the present day value. Our null result isconsistent with the recent measurements of King et al. 2009, (Delta mu)/u =(2.6 +/- 3.0) x 10^{-6}, and inconsistent with the positive detection of achange in mu by Reinhold et al. 2006. Both of the previous studies and thisstudy are based on the same data but with differing analysis methods.Improvements in the wavelength calibration over the UVES pipeline calibrationis a key element in both of the null results. This leads to the conclusion thatthe fundamental constant mu is unchanged to an accuracy of 10^{-5} over thelast 80% of the age of the universe, well into the matter dominated epoch. Thislimit provides constraints on models of dark energy that invoke rolling scalarfields and also limits the parameter space of Super Symmetric or string theorymodels of physics. New instruments, both planned and under construction, willprovide opportunities to greatly improve the accuracy of these measurements.

An Observational Determination of the Proton to Electron Mass Ratio in the Early Universe