  Time-dependent properties of the speckled intensity patterns created by
scattering coherent radiation from materials undergoing spinodal decomposition
are investigated by numerical integration of the Cahn-Hilliard-Cook equation.
For binary systems which obey a local conservation law, the characteristic
domain size is known to grow in time $\tau$ as $R = [B \tau]^n$ with n=1/3,
where B is a constant. The intensities of individual speckles are found to be
nonstationary, persistent time series. The two-time intensity covariance at
wave vector ${\bf k}$ can be collapsed onto a scaling function $Cov(\delta
t,\bar{t})$, where $\delta t = k^{1/n} B |\tau_2-\tau_1|$ and $\bar{t} =
k^{1/n} B (\tau_1+\tau_2)/2$. Both analytically and numerically, the covariance
is found to depend on $\delta t$ only through $\delta t/\bar{t}$ in the
small-$\bar{t}$ limit and $\delta t/\bar{t} ^{1-n}$ in the large-$\bar{t}$
limit, consistent with a simple theory of moving interfaces that applies to any
universality class described by a scalar order parameter. The speckle-intensity
covariance is numerically demonstrated to be equal to the square of the
two-time structure factor of the scattering material, for which an analytic
scaling function is obtained for large $\bar{t}.$ In addition, the two-time,
two-point order-parameter correlation function is found to scale as
$C(r/(B^n\sqrt{\tau_1^{2n}+\tau_2^{2n}}),\tau_1/\tau_2)$, even for quite large
distances $r$. The asymptotic power-law exponent for the autocorrelation
function is found to be $\lambda \approx 4.47$, violating an upper bound
conjectured by Fisher and Huse.
