  The onset of thermalization in heavy ion collisions in the weak coupling
framework can be viewed as a transition from the initial state Color Glass
Condensate dynamics, characterized by the energy density scaling like $\epsilon
\sim 1/\tau$ with $\tau$ the proper time, to the hydrodynamics-driven expansion
of the quark-gluon plasma with $\epsilon \sim 1/\tau^{4/3}$ (or higher power of
$1/\tau$ for the boost non-invariant case). We argue that, at any order of the
perturbative expansion in the QCD coupling constant, the gluon field generated
in an ultrarelativistic heavy ion collision leads to energy density scaling as
$\epsilon \sim 1/\tau$ for late times $\tau \gg 1/Q_s$. Therefore it is likely
that thermalization and hydrodynamic description of the gluon system produced
in heavy ion collisions can not result from perturbative QCD diagrams at these
late times. At earlier times with $\tau \sim 1/Q_s$ the subleading corrections
to $\epsilon$ in $1/\tau$ expansion (terms scaling like $\sim
1/\tau^{1+\Delta}$ with $\Delta >0$) may become important possibly leading to
hydrodynamic-like behavior of the gluon system. Still, we show that such
corrections do not contribute to the particle production cross section, and are
likely to be irrelevant for physical observables. We generalize our results by
including massless quarks into the system. Thus, it appears that the apparent
thermalization of quarks and gluons, leading to success of Bjorken
hydrodynamics in describing heavy ion collisions at RHIC, can only be
attributed to the non-perturbative QCD effects.
