We study the physical origin of the low-redshift Ly alpha forest in hydrody
namic simulations of four cosmological models, all variants of the cold dar
k matter scenario. Our most important conclusions are insensitive to the co
smological model, but they depend on our assumption that the UV background
declines at low redshift in concert with the declining population of quasar
sources. We fmd that the expansion of the universe drives rapid evolution
of dN/dz (the number of absorbers per unit redshift above a specified equiv
alent width threshold) at z greater than or similar to 1.7, but that at low
er redshift the fading of the UV background counters the influence of expan
sion, leading to slow evolution of dN/dz. The draining of gas from low-dens
ity regions into collapsed structures has a mild but not negligible effect
on the evolution of dN/dz, especially for high equivalent-width thresholds.
At every redshift, weaker lines come primarily from moderate fluctuations
of the diffuse, unshocked intergalactic medium (IGM) and stronger lines ori
ginate in shocked or radiatively cooled gas of higher overdensity. However,
the neutral hydrogen column density associated with structures of fixed ov
erdensity drops as the universe expands, so an absorber at z = 0 is dynamic
ally analogous to an absorber that has column density 10-50 times higher at
z = 2-3. In particular, the mildly overdense IGM fluctuations that dominat
e the Ly alpha forest opacity at z > 2 produce optically thin lines at z <
1, while the marginally saturated (N-HI similar to 10(14.5) cm(-2)) lines a
t z < 1 typically arise in gas that is overdense by a factor of 20-100. We
find no dear distinction between lines arising in "galaxy halos" and lines
arising in larger scale structures; however, galaxies tend to lie near the
dense regions of the IGM that are responsible for strong Ly alpha lines. Th
e simulations provide a unified physical picture that accounts for the most
distinctive observed properties of the low-redshift Ly alpha forest: (1) a
sharp transition in the evolution of dN/dz at z similar to 1.7, (2) strong
er evolution for absorbers of higher equivalent width, (3) a correlation of
increasing Ly alpha equivalent width with decreasing galaxy impact paramet
er that extends to r(p) similar to 500 h(-1) kpc, and (4) a tendency for st
ronger lines to arise in close proximity to galaxies while weaker lines tra
ce more diffuse large-scale structure.