  We present a strong constraint on variation of the proton-to-electron mass
ratio, mu, over cosmological time scales using molecular hydrogen transitions
in optical quasar spectra. Using high quality spectra of quasars Q0405-443,
Q0347-383 and Q0528-250, variation in mu relative to the present day value is
limited to (Delta mu)/mu=(2.6 +/- 3.0) x 10^(-6). We reduce systematic errors
compared to previous works by substantially improving the spectral wavelength
calibration method and by fitting absorption profiles to the forest of hydrogen
Lyman alpha transitions surrounding each H_2 transition. Our results are
consistent with no variation, and inconsistent with a previous approx 4 sigma
detection of mu variation involving Q0405-443 and Q0347-383. If the results of
this work and those suggesting that alpha may be varying are both correct, then
this would tend to disfavour certain grand unification models.
