Investigations of redshifted clouds with the 21 cm line

21 cm studies, with the 305 m telescope at Arecibo, of QSO absorption-line clouds are described. A search for 21 cm absorption in 16 redshift systems exhibiting Mg II and Fe II absorption yield a single detection; at zsub(a) = 0.394985 in PKS 1229-02. The null observations are interpreted in terms of turbulent gas that is optically thick in the resonance transitions, but thin to 21 cm radiation. Occasionally a very opaque cloud with low velocity dispersion is present which gives rise to 21 cm absorption. The latter has little effect on saturated equivalent widths. Hence one cannot predict 21 cm absorption from properties of Mg II and Fe II absorption. Lα absorption, however, is sensitive to the presence of very opaque clouds, and a 21 cm absorption line was discovered at zsub(A) = 1.77642 on the basis of strong Lα absorption in MC3 1331 + 170. A search for 21 cm emission from extended H I envelopes in a complete sample of 28 spiral galaxies is described. The coincidence of 21 cm and optical absorption redshifts imply space-time invariance of certain physical constants throughout most of the observable universe. Because one of these depends on all the details of strong interaction physics, it is suggested that all physical laws are globally invariant. (Auth.)