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The variation of the dimensionless fundamental physical constant mu = m_p/m_e(the proton to electron mass ratio) can be constrained via observation of Lymanand Werner lines of molecular hydrogen in the spectra of damped Lyman alphasystems (DLAs) in the line of sight to distant QSOs. Drawing on VLT-UVES highresolution data sets of QSO 0347-383 and its DLA obtained in 2009 our analysisyields dmu/mu = (4.3 +/- 7.2) * 10^-6 at z_abs =3.025. We apply corrections forthe observed offsets between discrete spectra and for the first time we findindications for inter-order distortions. Current analyses tend to underestimatethe impact of systematic errors. Based on the scatter of the measured redshiftsand the corresponding low significance of the redshift-sensitivity correlationwe estimate the limit of accuracy of line position measurements to about 220m/s, consisting of roughly 150 m/s due to the uncertainty of the absorptionline fit and about 150 m/s allocated to systematics related to instrumentationand calibration.

QSO 0347-383 and the invariance of m_p/m_e in the course of cosmic time