  We present precise HI 21 cm absorption line redshifts observed in multiple
epochs to directly constrain the secular redshift drift dz/dt_o or the cosmic
acceleration, dv/dt_o. A comparison of literature analog spectra to
contemporary digital spectra shows significant acceleration likely attributable
to systematic instrumental errors. However, we obtain robust constraints using
primarily Green Bank Telescope digital data. Ten objects spanning z=0.09-0.69
observed over 13.5 years show dz/dt_o = (-2.3 +/- 0.8) x 10^-8 yr^-1 or dv/dt_o
= -5.5 +/- 2.2 m/s/yr. The best constraint from a single object, 3C286 at <z> =
0.692153275(85), is dz/dt_o = (1.6 +/- 4.7) x 10^-8 yr^-1 or dv/dt_o =2.8 +/-
8.4 m/s/yr. These measurements are three orders of magnitude larger than the
theoretically expected acceleration at z=0.5, dz/dt_o = 2 x 10^-11 yr^-1 or
dv/dt_o = 0.3 cm/s/yr, but they demonstrate the lack of peculiar acceleration
in absorption line systems and the long-term frequency stability of modern
radio telescopes. A comparison of UV metal absorption lines to the 21 cm line
improves constraints on the cosmic variation of physical constants:
Delta(alpha^2 g_p mu)/(alpha^2 g_p mu) = (-1.2 +/- 1.4) x 10^-6 in the redshift
range z=0.24-2.04. The linear evolution over the last 10.4 Gyr is (-0.2 +/-
2.7) x 10^-16 yr^-1, consistent with no variation. The cosmic acceleration
could be directly measured in ~125 years using current telescopes or in ~5
years using a Square Kilometer Array, but systematic effects will arise at the
1 cm/s/yr level.
