We report new upper limits on any possible long-term time variation of the ratio of the electron to proton masses, me/mp, the fine-structure constant, α, and the quantity α2gp(me/mp), where gp is the proton gyromagnetic ratio. These limits are based on extremely high precision observations of H2, Si3+, C0, and H0 in high-redshift quasar absorption lines. They amount to 95% confidence ranges of (-7.6 → 9.7) x 10-14 yr-1 for me/mp, (-4.6 → 4.2) × 10-14 yr-1 for α, and (-2.2 → 4.2) × 10-15 yr-1 for α2gp(me/mp), where the elapsed time has been computed for a cosmology with H0 = 75 km s-1 Mpc-1 and q0 = 0.5.
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A 1995 study studied this question.