  Understanding the origin of electron incoherence is the first step toward a
theoretical description of the non-Fermi liquid behavior of the high-T$_{c}$
cuprate superconductors. Such electron incoherence manifests itself most
evidently in the non-Drude behavior of the optical response of the system and
the anomalous density fluctuation behavior in the long wave length limit. The
spectral weight transfer related to such dissipative response, which is absent
in conventional Fermi liquid metal, has direct consequence on the dc transport
property of the system in the normal state and the superfluid stiffness in the
superconducting state. It is found that such electron incoherence remains
significant even in the clean limit and at low temperature and thus must be
attributed to the strong electron correlation effect in the cuprate
superconductors. Here we study such an intrinsic effect in the 2D $t-J$ model
through the variational calculation of its optical conductivity
$\sigma(\omega)$. We assume a resonating valence bond ground state as our
starting point and find that a significant portion of the total optical
spectral weight remains incoherent throughout the phase diagram. The optical
absorption is found to extend all the way to an energy of the order of the bare
band width. We find that both the total optical weight $\bar{K}$ and the
integrated incoherent optical weight $I$ increase monotonically with doping,
with their ratio $R_{incoh}=I/\bar{K}$ decreasing monotonically with doping.
Our results indicate that the majority part of electron incoherence in the 2D
$t-J$ model can be attributed to the electron fractionalization mechanism
assumed in such a treatment. We also find that the Drude weight deduced from
$D=\bar{K}-I$ scales linearly with hole doping, without any sign of a
non-monotonic behavior in the overdoped regime.
