  We analyze the statistical properties and dynamical implications of galaxy
distributions in phase space for samples selected from the 2MASS Extended
Source Catalog. The galaxy distribution is decomposed into modes $\delta({\bf
k, x})$ which describe the number density perturbations of galaxies in phase
space cell given by scale band $\bf k$ to ${\bf k}+\Delta {\bf k}$ and spatial
range $\bf x$ to ${\bf x}+\Delta {\bf x}$. In the nonlinear regime,
$\delta({\bf k, x})$ is highly non-Gaussian. We find, however, that the
correlations between $\delta({\bf k, x})$ and $\delta({\bf k', x'})$ are always
very weak if the spatial ranges (${\bf x}$, ${\bf x}+\Delta {\bf x}$) and
(${\bf x'}$, ${\bf x'}+\Delta {\bf x'}$) don't overlap. This feature is due to
the fact that the spatial locality of the initial perturbations is memorized
during hierarchical clustering. The highly spatial locality of the 2MASS galaxy
correlations is a strong evidence for the initial perturbations of the cosmic
mass field being spatially localized, and therefore, consistent with a Gaussian
initial perturbations on scales as small as about 0.1 h$^{-1}$ Mpc. Moreover,
the 2MASS galaxy spatial locality indicates that the relationship between
density perturbations of galaxies and the underlying dark matter should be
localized in phase space. That is, for a structure consisting of perturbations
on scales from $k$ to $ k+\Delta {k}$, the nonlocal range in the relation
between galaxies and dark matter should {\it not} be larger than $|{\Delta {\bf
x}}|=2\pi/|\Delta {\bf k}|$. The stochasticity and nonlocality of the bias
relation between galaxies and dark matter fields should be no more than the
allowed range given by the uncertainty relation $|{\Delta {\bf x}|| \Delta{\bf
k}}|=2\pi$.
