Astrophysical Limits on the Evolution of Dimensionless Physical Constants over Cosmological Time

We report new upper limits on any possible long-term time variation of the ratio of the electron to proton masses, $(m_e/m_p)$, the fine-structure constant, ($\alpha$), and the quantity $\alpha^2 g_p(m_e/m_p)$, where $g_p$ is the proton gyromagnetic ratio. These limits are based on extremely high precision observations of H$_2$, Si$^{3+}$, C$^0$ and H$^0$ in high-redshift quasar absorption lines. They amount to 95\% confidence ranges of $(-7.6\to 9.7) \times 10^{-14}$ yr$^{-1}$ for ($m_e/m_p$), $(-4.6\to 4.2)\times 10^{-14}$ yr$^{-1}$ for $\alpha$\ and $(-2.2\to 4.2) \times 10^{-15}$ yr$^{-1}$ for $\alpha^2 g_p(m_e/m_p)$, where the elapsed time has been computed for a cosmology with \hnought = 75 km s$^{-1}$ Mpc$^{-1}$ and \qnought = 0.5.